We primarily use NUCs if we need a low cost computer. Mainly the 7th and 8th generations. Any of them will run TouchDesigner but of course you’ll be able to do a lot more with the i7 versions. They also have a version without the enclosure if you’d like to build your own.
If you need a GTX card it seems like the ZOTAC computers are a pretty decent choice. I don’t have much experience with them but I’ve heard good things.
Another thing you might consider is building a machine with a mini-atx motherboard. Then you could get a full size graphics card and maybe even a capture card. This case is pretty decent for that:
I’ve got TD running on an Up Board but it was a pain to set up and it isn’t particularly reliable or fast. Hard to beat the price though ($89):
Haven’t tried the Up Squared yet but I’m assuming it wont be any better than a NUC.