John, in addition to the many answers you are getting here, I suggest that you go to
Most, if not all, current 7 channel radios these days are computer controlled. One of the features you will get is multiple model memory. The transmitter can remember the trim and other setup settings for multiple planes. The exact number varies by transmitter. Your first setup should be a package which includes the transmitter, receiver, servos, battery, switch harness, etc. All of this equipment can be used in multiple planes. However, as you've already heard, when you get to the point where you have more than one flyable plane, it's not practical to move the flight equipment from one to another. For this reason you will start to "collect" additional flight equipment. This equipment needs to be compatable, but does not have to come from the same company.
If you are on a budget, there are less expensive, but perfectly viable trasmitter choices for getting . The simplest is a basic 4 channel. This will cost around $100 for the entire radio package. Even if you later decide to go with a 7, 9, or 14 channel system, the flight pack portion of the basic 4 channel system can still be used. If you spend a little more you can get a 6 channel computer radio. These provide some of the benefits of a computer setup such as electronic trim, end point adjustments, throttle cutoff, multiple model memory, etc, but at a lower cost than the fuller function 7 channels. One of the best deals, IMO, right now for a 6 channel computer radio is the Futaba 6EXA at Tower. When you subtract the rebate, discounts, and gift certificate savings, the net price is $130.
I find Tower Hobbies to be one of the "best" places to buy. Their prices are usually pretty good, their shipping is very predictable, and their web site is well organized. However, they don't have everything. For someone just starting out, they should have everything you need. As has already been mentioned, you should also consider buying at your local hobby shop (LHS). The prices may be a little higher, but being able to ask questions makes it worth the difference. However, if your LHS is really just a toy store that happens to carry some R/C stuff, it's usually not worth bothering.
I also suggest getting in touch with the nearest club before you buy anything. Most clubs have training programs. They will put you in touch with one of their instructors who can give you some adivce on radio, engine, and plane selection, as well as giving you their opinion on the LHS. If you're in the US, to locate a club, go to the AMA's club locator: