There are a number of TT's that you can get through online dealers such as AudioAdvisor, MusicDirect, Acoustic Sounds and KAS that will sound good in the price range you have set.
Not knowing what type of Preamp you have or if it has a phono preamp built in you may have to go for turntable with a moving magnet cartridge that would have enough output to drive the preamp. With the moving magnet in the turntables below. I would ask the question about needing a phono preamp.
If you don't have enough output or a phone preamp that built in then you're looking at the additional cost of a phono preamp and cables.
Here are two from Music Direct(I have not financial interest in them by the way).
Sometimes you can pickup a good deal on Audiogon or Craigs List for the like an older VPI TT
HiFi is a pretty slippery slope when it comes to getting good quality and the law of diminishing returns applies to the equipment and sound. The more you pay doesn't mean that you will get a corresponding increase in sound.
If you just want to experiment to see if you want to get back into vinyl or have old record one of these three will do the trick.
Those are my thoughts for what they are worth.