Help…looking to buy turntable

Rega +1

Tonearm pre-installed and suggested carts make them easy. Oh yeah, great sound too. 

VPI Cliffwood or Player - entry level VPI tables, both with cartridge pre-installed. The Player lists at $2000 (over your budget, but does also have a built in phono preamp and headphone jack).  The Cliffwood is $1500, but you'll most likely need a phono preamp...Musical Fidelity V90-lps at around $300 is a really good entry level phono stage that supports both MM & MC.

I'd look at a Technics sl1200C ($1200 with a decent Ortofon 2M Red cart).  It has a built-in phono pre, but for an additional $129 you could get a Schitt Mani and that should keep you going for a while.
The tonearm has a SME style head shell connector that makes cart changes easy and fun.  The 2M red is a good starting place (I have a Hana SL on my 1200 GR, a remarkable cart for the price, but I also have a Mofi MasterTracker that sounds different but just as good, and several Grado and Shure carts that are fun to rotate in).  There are many carts between $200 – $800 that would work well with this table!

I have a music hall MMF-7 with Goldring Eroica H MC cartridge installed. Spent most of its life in its original box. Enjoying it now but thinking about a VPI Prime. Would sell for much less than your budget. Pretty sure this isn’t the forum so will save details in the event you want them. 
 

Regardless, many good suggestions above. 

I'm going to go back even further and suggest a Dual 701 semi-automatic turntable (it lifts at the end of play).  Duals are very tricky to service and their are not many folks who can do so with expertise these days, so that is a fallback.  But if the unit works well, it cannot be beat.  Best direct drive unit of its day (075); best arm of its day dampened resonance and spring driven in balance, accurate anti-skate.  Heavy duty dynamically balanced platters.  Second best is a 704, which has a slightly lower-spec Pabst motor but an advustable VTA added.  You can pick up a 701 for $400-500 and a 704 for $280-380, which leaves plenty of room for a cartridge.  You can easily mate it with a quality MM cartridge and come in under your dollar threshold.