You are talking about a turntable for some very good speakers and associated system, so here are three suggestions:
1. Linn Sondek LP-12 (preferrably with Valhalla and Cirkus mods/revisions) and Ittok LVII tone arm
2. Thorens TD-125 MkII with SME 3009 S2 tone arm
3. Technics SL-120 and SME 3009 S2
It would take some looking to find these in used but excellent condition but they could be found; all 3 could provide excellent turntable and tone arm performance and with some good shopping could be done for $1k or less (the Linn would be the toughest to meet your budget but might be doable).
If you need a cartridge to fit within this budget it would be tougher but it might still be doable. You should probably pick the cartridge first to make sure it will work with the tone arm or you could start with these tt/ta combinations and live with whatever cartridge fits in your budget for now. Many people will have opinions on cartridges, it is a topic for another thread - including MC or MM. MC will be easier on your budget but there are some strong MC cartridges out there.
PS, if you haven't tried any Bill Evans LPs, track down a copy of his albums, including Qunitessence - you will enjoy the jazz