Firstly I would say find a local club and see what radios the instructors use.
Look at:
http://www.modelaircraft.org/
to find a club close to you.
Then buy whatever brand radio the majority of the instructors use. It makes no sense buying a JR radio if the instructors only use Futaba.
Then after making the brand choice I would also suggest buying as much radio as you can afford. Definitely do not buy the 3-channel system.
At a minimum you will need 4 channels. Aileron, Elevator, Throttle and Rudder.
Then a little bit further down the track you will want 6 channels to add retracts and flaps.
If your budget is around $200-$250 as you mention, then you will also want to buy a computer radio. This way you can have one transmitter and store model configurations in memory so you can fly more than one plane from the one transmitter (1 at a time of course!
)
When I started out I bought a Futaba T6XAs and am now wishing I bought something better. It cost me around $230 when I bought it.
Moving up to a better radio does not only add more channels, but it adds programming features in the radio too. My 6 channel radio has enough channels to fly a heli but it is a little lacking in the heli programming department.
Another tip! When I started I wasn't very interested in helis. Now for some reason the bug has bitten me and I want a heli. So it is even more important to get the best possible radio as you never know where this hobby will take you and it is a real annoyance having to shell out more cash to replace something that you should have bought properly in the first place.