Help…looking to buy turntable

I’m assuming your $1200 budget includes cartridge.  I would consider it wise to get the best possible TT, and then get the best possible cartridge without going overboard.  In other words, don’t put a souped-up engine in a Ford Pinto.  
The suggestions for the Music Hall Classic Seem very sound (no pun intended) to me.  It’s also a very visually appealing TT, if that matters to you.

You could install (and would have to learn how to optimally calibrate/align) say, an Ortofon Bronze cartridge on that bad boy, and, with tax, be around $1100.  You could opt for the Ortofon Blue and be around $900.

I’m only suggesting Ortofon cartridges because they seem like good bang-for-the-buck cartridges. On an old TT, I had a low-end 2m Red which, back then, retailed for about $100.  Surprisingly good cartridge.

Other posters here, I wouldn’t doubt, may have better suggestions for cartridges in, say, the $200-$500 price range.

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.