Helicopters
All prices listed in US Dollars.

I recommend these helicopters for beginners (and experts, actually) based on value (price vs. performance) and stability (ease of flying in most conditions); the Thunder Tiger Mini Titan (electric), the Align Trex 600E (electric), the Align Trex 600N (nitro), and the Thunder Tiger Raptor 50 (nitro). These helis can be tamed down with small control inputs (set in the radio) to make them respond slower. By simply changing the radio settings, these machines can go from mild to wild with the flick of a switch, allowing eye-popping 3D maneuvers when your skills are itchin' to show-off. If you are an absolute beginner with zero RC experience, and want to try your hand flying a real model right away, try the E-Flite Blade CX (electric).

The Thunder Tiger Mini Titan is a small electric powered helicopter, which is available in several versions. A kit including a capable motor and speed control costs ~$200, and can be assembled in a handful of hours. Other versions are pre-built, at slightly increased price points. I've found this to be a dynamite model. It has both stability in windy conditions (not often associated with small helis) and it also can really perform 3D aerobatics if you turn up the juice. For this model I recommend JR 285 digital servos, a Futaba 401 gyro with digital tail servo, Thunder Power batteries, and Radix rotor blades. I leave everything else stock, including the the motor and speed control. Beginners will find this to be a smooth flying heli that is suprisingly forgiving in the wind for its size. It's also durable, and parts are cheap.
Cost - $200 for the kit with motor and speed control

The Thunder Tiger Raptor 50 Titan is a highly refined model which offers exceptional durability, agility, and stability. All Raptors fly nicely, and parts are available world-wide. I've written a review of the first version of this helicopter, which can be found here.
Kit Cost - $400

The Align Trex 600E and Trex 600N are excellent helicopters for the beginner, yet can be setup to allow amazing 3D maneuvers. These are both more capable performers in the hands of an expert than the Raptor Titan, but also fly nicely with reduced control throws. Parts are widely available, and inexpensive. The 600E electric showcases the clean, powerful flight that is attractive, but also does not allow for long flights due to battery capacity (about 5-9 minutes flying time, depending on load). The 600N is a very lightweight 50 class nitro model that shares the same basic mechaincs with the 600E.
Kit Cost - $400 to $620

The E-Flite Blade CX is a small electric powered coaxial rotor helicopter, which costs $190, completely ready to fly. The sensational performance (you can fly this - even if you've never flown anything RC before!) and durability of this model puts it on my list for beginners who aren't ready for the expense of a larger heli. The Blade CX is amazingly stable, owing to the solid stability of the twin rotor system. Indoor hovering maneuvers typify a Blade CX flight - it isn't agile enough for forward flight. Included with the Blade CX is a 4 channel transmitter, 2 servos, gyro, 2 speed controls, 2 drive motors, receiver, rechargeable lithium-polymer battery pack with charger, and the assembled (and factory test flown!) helicopter. You'll only need to supply 8 AA batteries to get it airborne. Buy the Blade CX if you are a new pilot looking for an easy to hover model.
Cost - $190, complete, ready to fly

If the cost of the hobby is not a concern, I suggest purchasing a larger helicopter. 60 to 90 sized helicopters are a bit easier to fly due to the stability of a heavier machine with a larger rotor disc. Bigger helicopters usually have a higher power to weight ratio, and they can perform some of the more demanding maneuvers with ease. Also, because of their size, 60-90 powered helicopters are easier to see in the air. However, a 60-90 sized helicopter costs quite a bit more than the smaller models, and crash costs are much greater. Since the models are heavier (and can fly faster), crash damage can be more extensive. Unless money is no object, stick with the models listed above.

Radio Systems

There are many radio systems that are excellent choices, and these days, most all work very well. I prefer Futaba radios, although JR radios are my second choice. An entry level helicopter radio will have at least 6 channels of control. 72mhz radios are quickly being replaced by the newer spread spectrum 2.4ghz technology, as it offers several advantages in eliminating frequency conflicts and reducing possible interference from RF noise prone environments. For most beginners, I recommend the Futaba 7C, as you can use the features in this radio for years to come. The Spektrum DX7 is a very popular 2.4ghz radio, that is perfect for any heli pilot.
Cost - $350

Gyros

The Futaba GY-401 is a top-performing gyro set. This isn't the cheapest gyro option, but predictable tail control makes learning to fly helis much easier. It features rate mode and heading-hold modes, which are remotely switchable. Most beginners find the heading hold mode to be very helpful, as this feature will keep the tail stationary regardless of wind or torque changes. This gyro is also available with the special Futaba 9254 digital high speed servo, which maximizes the gyro performance.
Cost of the GY-401 - $140
Cost of the GY-401 + 9254 - $220

Engines

Historically, OS Engines are an excellent choice. They run very smoothly, with plenty of power. The OS .50 Hyper is a perfect match for the Thunder Tiger Titan and Align Trex 600N copters listed above.
Cost of the OS .50 Hyper - $200

If not already included with your engine, you will need a glow plug. It's a good idea to have a couple of spares, as sometimes they will need replacement. Most pilots prefer OS #8 glow plugs, but I've had good luck with other brands as well, such as J&Z glow plugs and Tower Power glow plugs.
Cost - $3 to $6

Exhaust Mufflers

The Raptor Titan listed above includes a high quality, one-piece aluminum muffler in the kit. Align also markets a muffler for the 600N.

Flight Line Equipment

Most pilots use a field box to carry all of their flight line equipment, but some find that a simple plastic tackle box, or hardware tool box works fine too. I use a tool case which has enough room for the transmitter, starter & battery, voltmeter, small parts and essential tools, and it fits easily in the car.
Cost - $20 to $50

You will need the following items to assist in getting the engine running: an electric starter, a battery and battery charger for the starter, a glow plug ignitor, helicopter specific fuel, and a fuel pump.
Cost - about $100

Knowing if your on-board batteries have enough power for the flight can mean the difference between flying and crashing. Monitor your battery with a load-testing voltmeter, available in either an analog style or digital style.
Cost - $11 to $25

I recommend using Morgan's Cool Power Helicopter fuel, in either the 15%, 20%, or 30% blends, or Magnum 12.5% or Heli-Plus Helicopter fuels.
Cost - about $20 per gallon

For electric helis, I recommend Thunder Power Lithium Polymer batteries, and chargers.

Tools

Ball link pliers are needed to remove and install the plastic links to the control balls. This particular brand distributed by Ace works very well.
Cost - $17

A ball link sizing tool is necessary to properly fit the plastic links to the control balls.
Cost - $16

When setting up the control system, it is important to check the main rotor blade pitch and flybar paddle alignment, with a pitch gauge and flybar paddle alignment gauges.
Cost - $30

Balancing the main rotor blades will ensure that your helicopter will not shake itself apart. Check this with a rotor blade balancer.
Cost - $23

When assembling the engine and transmission, it is often necessary to use a piston locking tool to keep the crankshaft from rotating.
Cost - $8

Ball link driver tools can be very handy when assembling the linkage rods.
Cost - $9

You will also need a selection of modeling type tools - small screwdrivers, metric allen wrenches and allen drivers (1.5mm, 2mm, 2.5mm, 3mm), a metric socket set, scissors, pliers, cutters, drill & drill set, exacto knives, dremel tool, super glue, lock-tite, etc. The use of Lock-Tite on the hardware fasteners is essential! Use the "blue" grade Lock-Tite. I prefer to use Tamiya blue gel thread lock as it remains a bit gummy (Lock-Tite brand thread locker sets up like glue) and makes it easier to remove the fasteners when needed yet holds fast.
Cost for tools and supplies - $varies

I've found that an empty hair spray bottle filled with isopropyl alcohol can be very handy for cleaning the chopper. The alcohol does a good job at cleaning up the grease and grime, plus it won't harm the electronics, nor burn onto the engine or muffler.

Training Gear

The best performing training gear is the Roto-Pod, which is a must have for beginners. This device gives the helicopter landing gear a bigger footprint, which helps prevent the heli from tipping over. The design allows for a certain amount of tilting, which lets the pilot get a feel for the cyclic control without actually taking off. Once you become comfortable enough to get the copter airborne, it also provides a bit of springyness to dampen rough landings.
Cost - $50

The Roto-Pod is far too big and heavy to use with the tiny Blade CP or CX helicopters. Instead, use the Blade CP Training Gear.
Cost - $10

Extras

This is the first item that you should purchase. Ray's Authoritative Helicopter Manual is the rc helicopter pilot's bible. If it concerns model helis, it's in this book!
Cost - $20

Most pilots find that using a simulator is paramount in learning to fly model helicopters. I like RealFlight G2. If you have a capable computer, you might consider buying this simulator and "trying" your hand at the hobby before actually purchasing a real helicopter. It is common for new pilots to have several hours of "flight time" on the simulator before they fly a real model. This software program is $200 but will pay for itself in the first 30 seconds that you use it. Crashing real helicopters is expensive. Crashing the simulator is free. Generally, beginners that use a simulator are literally years ahead of those who don't. I recommend buying the USB version with the included "transmitter" controller, as using your own real rc transmitter is not really advantageous.
Cost - $200

Edit: The latest verion of Realflight is something like version 4.0?? It's still the best buy IMO compared with other sims, buy I haven't upgraded mine yet.

Eric's RealFlight G2 Helicopter Models

The files below are my "raptor" setups for the Realflight G2 rc simulator. There are 3 files. They are named Raptor30-Eric.heli, Raptor50-Eric.heli, & Raptor90-Eric.heli. One flies like my Raptor 30 (with OS 32, Weston pipe, 550mm CMT fiberglass blades, 30 % CP fuel), one flies similarly to my Raptor 50 (with OS 50, TT muffler, 600mm Funkey carbon blades, 30% CP fuel), and the last one flies similarly to my Raptor 90 (with YS .91, CY Muscle Pipe II, 710mm TT carbon blades, 30% CP fuel).

I hope that this list has been helpful!