With a computer radio, you get a certain amount of memories. Each memory will hold whatever settings you set up for that particular plane. Some radios such as the Hitec Flash 5X, which holds 5 planes in memory, list each memory by number, 1 thru 5. You need to come up with a way to remember what number matches what plane you set up. In one case where I was flying a plane with a Futaba 6XAS (also only saves the memory by number) I just stuck a #5 on the top of the fuse of my Uproar so I would know that it was on memory 5.
I also wrote the numbers and planes along the shelf above my bench for quick reference at home. Not a good way to do it tho.
Best way would be to tape a list to the back of your transmitter.
Some other systems will allow you to enter an alphanumeric for each plane so you can actually put the plane's name on each memory. My Futaba 9C does this.
Now, you do not need a computer radio to use your transmitter on different planes but you will have to re-adjust the trims on the transmitter each time you fly a different plane!
Whether you use a computer or non-computer system, after the initial system purchase which will include transmitter, receiver, battery pack for both, switch harness for the plane, servos, wall charger, some hardware for the servos and so forth, for each plane after that you purchase what is called a Flight Pack. This will include all the radio equipment for the plane but no transmitter. Be sure to get the flight pack on the frequency of your original transmitter!
You can also buy every item in a flight back individually if you wish.
Whatever brand you decide on, I would advise you to purchase a system with at least 6 channels. A 4 channel system will work fine now, but when you move up to flaps, dual servo ailerons, etc, you will wish you had those other 2 channels.