$1200... What would you buy?

First question, does your receiver have a phono section?
If not you will/may need a phono preamp possible, depending on the cartridge you choose.
Second, rather than spending it all, why not try say between 550-850 and look for a good used Rega P3 or MusicHall MMR-5 or 7. Others will have other choices.
Analogue, is my passion in this hobby, and can take a fair amount of time and effort to get it right. My thought would be to start with something that is fairly easy and if you choose to back out won't cost you to much on the resale,if anything.
Definitely plunge on in to the deep end, but one can always upgrade, and the accessories/necessities are quick to follow up. Namely record cleaners, their solutions/enzymes, pads, brushes etc. All sorts of useful but not used a lot little tools, clamps, weighing scales, static brushes, and on it can and may well go. Perhaps mania is a better description than passion for me.
Music is meant to be heard and enjoyed above all else.
Play around see what it out there on vinyl and above all else have fun

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......

Botit, Yes, the older Denons are a beautiful table,and i have myself a lesser one on ice as a second table, a DP-2550, with a retro-fitted AQ PT-8 Arm.

Downside of the Denons you mention, is that these Tables are getting up in age, to find a mint one, without Plinth Scars, and Rashes becomes harder, and harde, they'll be top dollar for an el minto example, and the other, even larger possible problem with these, is electrical problems, they were quite sohisticated electronically, and were prone to speed stability problems, with thier magnetic strip on Platter, Sensor, and an array of electronics to make it all happen.

If I had that sort of money,was looking and perhaps a little more $$$ just in case, I would perhaps keep an eye out for a mint VPI Aries 1, that possesses the original Lead Filled Black Acrylic Platter. If it has the JMW 10.5i Arm, all the better.

There's of course a myriad of other fine Tables out there to be had used.

The other gents here have brought up some fine points, and I hope they have helped you to narrow down your choices. Mark

Agree with the used P5 suggestion - you could also find the Bellari tubed phonostage for under $200, if you needed one, and it matches up nicely with the P5.