New: Technics SL-1200MK7 for $999 (you may even be able to get it for less if you call Guitar Center). This is a table onto which you could install your preferred cartridge, set it, and forget it. Just enjoy the music. The build quality likely won't *feel* quite as nice as a MK2, but I have no doubt that it will sound excellent. It doesn't have a hinged dust cover, in case that's important to you. For that, I would recommend the SL-100C from Amazon Germany, which comes to just over $1k shipped after the exchange rate.
Used: There are many options here, but you have to remember that condition is quite variable. Obvious cosmetic and functional issues aside, the older a turntable is, the more likely it will require servicing sooner than later. Many units from the 70's and 80's could potentially present issues at any moment, without at the very least being examined by a qualified tech.
It can be very fun to buy from Japan, as the used market there is far more extensive than here. Many models that are uncommon or were never sold in the US are plentiful there. Some Japanese sellers sell internationally on eBay; this gets you more buyer protection, but the prices are generally higher and the units not as nice cosmetically. If you become well-acquainted with Buyee or another proxy shipper, it is possible to find some really good deals on stuff through Yahoo Auctions. You can learn which sellers are bulk/junk (untested) audio sellers, which sell nice but unserviced items, and which sell serviced and/or mint items. Of course, you have to take into account shipping costs to the US, which can range from $150-400 depending on the unit in question. You also need a stepdown transformer for 100V units. If anyone has further questions regarding this process, I'd be happy to help.
I second Mister Pig's DP-75 recommendation, as well as the DP-80. Of course, aside from the DP-75M model, you would need a separate tonearm.
This seller frequently lists Kenwood KP-9010/KP-1100 turntables in excellent condition. The auctions tend to end around or under 90,000 JPY, or around $700. They go a bit overboard with packing, so shipping would be on the expensive side, but it should come to around $1k using Buyee:
https://buyee.jp/item/yahoo/auction/s1059301112
You could also likely find a used SL-1200MK2 for somewhere under $1k in the US from a fellow home user.