Sometime in the next three months or so I plan on getting a new stereo. It would be somewhat of a budget stereo but an improvement over my shelf system. Right now I have a cheap Sony Turntable that cost about $100, I'm not by it so I don't know the exact type. Is there any turntables around $200 or so and would I see any improvement ove the one I have now?
Your best bet may be to search for a good used turntable. There are plenty of them out there. Right now, I'm using a Dual 506 (with a Stanton 681eee cartridge) that I got at the Salvation Army for $15 (in mint condition no less, even the dust cover!) Three good vintage "budget" names to look for are Dual, Thorens and AR. Happy hunting!
Duals were very well-built. I used to have a CS-5000...great little turntable. Look for belt-driven models.
If you are willing to go a little over $200, try a Music Hall MMF-2.1. I bought one of these when I was getting back into vinyl 3 years ago. It's belt driven, has a Goldring cartridge and is about as close to plug & play as you can get. For the price, the sound is outstanding. List price is $299, but if you search the net you can definitely find it for less. Music Hall also offers a lower model, the MMF-1, but I have never heard this TT. It lists for less than $200.
I'll be brief here... Get as much as you can, because the smarter [and sometimes] more money you put in your phono rig, the better. I'm not saying one should go into a high end VPI form nothing with a small budget, but push the limit from the start just a little. You will be a LOT happier once you've listened for a while.