I recommend the Bang & Olufsen turntables, from about the mid-1980s on, as a great starting point. No, they're not the last word in performance, but they are suprisingly good, and setup is extremely easy. Soundsmith has a variety of good cartridges available for them, and all you need to do is plug in a cartridge, and set the vertical tracking force. No VTA, anti-skate, damping, azimuth, overhang, cartridge-tonearm matching, etc. etc. to worry about . . . and you can set them on just about anything, and they don't have feedback problems, and they don't skip.
If you go to Beoworld.com, they have a complete breakdown of models, eras, etc. You could pick up a used Beogram RX2 or TX2, a new Soundsmith SMMC4 cartridge, a Creek OBH-18 phono preamp, and a few good bottles of wine all well within your budget . . . and when you outgrow it, it's perfect for a second system.