Not asking too much. $250 for a turntable, $250 for powered speakers.
If you are buying new, I still stand by the Audio Technica LP120. I have owned the turntable and have set it up for a few friends' systems. Go to any Guitar Center or professional DJ/ music shop if you wish to audition it.
You may save some bucks if you buy a used/ vintage TT, but you will need to know how to perform basic clean-up and lubrication duties. Your call.
As for powered speakers, there are several companies out there to choose from ... Audio Engine, PSB, Emotiva, Klipsch. They are only going to play so loud, so for a small room system, you will be fine.
See, not so tough.
Rich