I have personally shot 2 bows all set up in the $300-$350 range. One was a Martin Tracer Mag and the other was a Fred Bear TRX. Both are fine bows for the money.
The Martin is short, smooth, light and accurate. I wish it had a better grip and a little more speed but it is plenty of bow to kill a deer any day.
The TRX is a really nice bow..........I would still own it.......but I let my brother have it because he was on hard times and being with my family in the woods is more important then any bow.
He had an old crappy bow and couldn't hit the ocean if he was standing in a boat. Almost instantly his shooting improved about 80%.......and now after a year with it he is a dead eye. He took a 6pt with it last year and I took a 6pt with it the year before..........so far it's 2 for 2
I like the split limbs design on the TRX and it is faster then the Martin but accuracy wise I would say they are as good as the shooter.
Both bows are very quiet.
Check them out if you get the chance............I know your options are limited but see what you can do.
No matter how far you have to drive it will be worth it if you get to shoot a bunch of bows and see which one REALLY fits you well............I have held a lot of $700 bows that I would NEVER buy and some $300 bows that feel great.
Good Luck