$1200... What would you buy?

Uru975 has some nice ideas. However, I wouldn't go cheaper to start. Buy something like a Sota with an ok arm and a decent cartridge. The table can last forever. If you really like it, you can always move up to a nicer arm or nicer cartridge. With a Sota, you can get away with a $99 ortofon or shure or Grado and it will sound nice. If you splurge and move up to a $300 Goldring, it will make a huge difference. The nicest part, if you chose to move up again to something like a clearaudio it will make a big difference again.
Don't forget quality toys like a clamp, scale and cleaning solution or system. Yep, these can run you a lot more money.
Once you have all of that, time to replace the stock arm with something exotic also.
Phono pre amps make big differences also.
Get it? We just started with a $600 rig and you now have something worth $2500 without having to replace the table at all. Wait until you send it back to Sota for upgrades too. You can do similar with other brands such as VPI.
HAVE FUN

Get a used MMF-5 as a starter table it originally came with that $300 crtridge .The old MMF-5 came with a GR1021 a moving magnet by goldring.As well with a clamp, cover etc all set up.
People it appears think they want to go analog. After giving it a go, they then, for any number of reasons, decide it isn't their cup of tea. So the MMF-5 a well known starter comes around for sale with some regularity.
The only warning as the owner of such a table is that it is far from the more detail retreiving tables, especially the tables which use MC carts.
The MM cartridge in general requires less of an incredible phono preamp. In fact if you have a classic preamp or in your case receiver, an MM phono input was a standard fixture.
It is a simple table and perhaps others are more detailed at that price point which was about $500-600 new. The current MMF-5 offerings from Music Hall are now near a kilobuck. I would skip it at that point but used it shouldn't legitimately cost you a lot more than $300. That is the price of the original incarnation not a 5.1. The 5.1 bought you some nice trimmings. The 7 adds plinth mass, and a heavier real dense acrylic platter, as well as a step up on the Goldring cartridge ladder, all that adds up to a lot more money. You won't find any in the $400 range. Unless they tore out the arm board and cart. leaving you limbless and paying out the shnozola for a cartridge.
My own next move was a VPI Scout with a $700 cart (680 OK close enough) and the JMW9 arm in a factory package. It is night and day different and very good. plentiful bass and highly detailed. The Dynector 20X HO MC cart I chose is flexable. It can be used with an MM phonostage but the current model is a medium output MC that will require an MC capable phono stage. These can cost as much as you want, of course, dependent on what you decide is aceptable.
All of them tube or SS have to be dead silent not so easy to do.
$1200 should get you the Scout setup. An ideal buy would be from a person who used it only occasionally and not long enough hours for the opportunity to ruin the cartridge. I got mine at a closeout price. It is as much table as I think I will want.
Avoid the temptation of a quick impulse to get a semi automatic from back in the day. The only thing they do automatically is stop working.
I suggest experiment first as cheaply as you can to see if you even care for the routine. If you know you are definitely in love with it then... I would and did get a Scout or the likes e.g. SOTA whatever. Then start figuring out what you are going to do for a good MC phono stage?
Good Luck on your adventure .
I play vinyl but I am far from an analog devotee. Be careful not to sell your other sources.

as you've mentioned, a mint dp60 or 62 is great.

2nd the Rega,but look for the 5/7 used and pop in a Glider or Blue Point special.

Given your system, I'd try to set a much lower $$ limit on the TT. I sold a Rega P25 a few years ago (no cartridge) for $500. I assume a P3 would be less. Start out small, $300-$500 for a used TT & cartridge......