For someone starting out I usually recommend just buying the Futaba 4YF at around $120. It's got the 4 channels you will need for a trainer type plane. Even if you decide to buy a more expensive transmitter later, the flight pack from the 4YF will still be useful.

Since your budget is higher, the 6EXA gives you some additional features that can be used on your trainer plane like electronic trim, end point adjustments and throttle cutoff. When you build your skills a bit you might want to start using dual and exponential rates, and multiple model memory. You can usually get this radio for $150 or less at Tower.

However, you said your radio budget was $250. In this price range you can go for a 7 channel, such as one of the Futaba 7C models. Some additional features include memory for more planes (and the ability to name the planes, rather than numbering them), dual rates on more channels (the 6EXA only does ailerons and elevator), more mixing features, support for helicopters, etc.

The thing that determines interoperability between plane and radio is as you guessed, the servo. And yes, the number of servos needed is dependent on the plane. Most systems in your price range come with 4 standard size servos, and it's easy to add more later. Fortunately, the size of the standard servo has settled down enough that most planes between .25 and .60 have trays that will fit a standard servo of any brand. If the holes in the servo tray are too small, you can usually enlarge them, if they are too big, you can usually replace the tray. So, your biggest decision is really to select the system that has the transmitter that best fits your needs for the next 3 to 5 years. Go to Tower Hobbies, Horizon Hobbies, and the manufacturer web sites for more information.

The last question you asked is what plane? Answer is just about any ARF trainer out there will do. If you like smaller size planes, or have limits on the space in your car, shop, etc, there are some trainers in the .15 to .25 size that would do fine. Note, I am biased toward this size because they use less fuel, less shop space, and are easier to transport. I can get 3 or 4 .25 size planes, with the wings on, in the back of my Explorer. I even got 3 inside my Sebring convertable last weekend, and 2 of them still had the wings on. However, the typical recommendation will be to get a .40 size trainer, and more options are available than the smaller size. I suggest not agonizing over the trainer decision. They are all similar, most of them will do the job, and it's likely to get beat up when you are learning, so it's better to not have any emotional or financial ties to it. I think the Tower trainer represents a good value. There are others in this price range that will also work. For the engine, choose a decent .45 (or .46, .47, etc) ball bearing engine. This will work well in the .40 size trainer and will transfer to many other planes once you're finished with your trainer.

Hope this helps...