What to look for in a good turntable???

Cartridge is most important. The overall character of the setup will be determined by that choice> shelter 501 would be my top pick At $800 bucks it sounds like a lot to spend on a starter table. It's not. You can live with this cartridge until you are ready to spend in excess of $4000 on a table.
Arm next Clearaudio Unify or Graham Robin At around $800 these are it. If your not ready to spend that much yet; look at Rega 250 300's.

Table : look for Acrylic platter minimum 30mm 50-70 better; isolated motor; spit plinth. The Clearaudio champion is a great place to start; because you can upgrade it all the way to a Champion Level II Base price $1000
Basis also offers a similar upgrade path starting with the Basis 1400

Good luck
Mike

WARNING! The following is the biased view of a DEALER!

The most important thing is that regardless of the components you select, they be installed and setup properly, and that they perform well together as a system. Professional setup is different than just mounting and aligning the cartridge. Choose a dealer who you know has the knowledge to perform a full professional set up.

As for the hardware, The SOTA Comet-III/250 table and arm with Grado Statement Series Platinum cartridge, and Grado PH1 Phono Stage is an amazing vinyl system that delivers far more than you'd expect for $1250. And everything except the Rega arm is made in the USA... Harry

Ewe all know what the Psychic uses...

Try A VPI Scout.1500.00 list,1350.00,discount. Will give you another perspective into what music should sound like.