I was under the impression that brand-name models don't have separate IGP video ports in addition to discrete graphics ports, but I could be mistaken.
Yeah, that sounds odd as it's on the back of the motherboard.
Buy any PC with only IGP out and has a 16x PCI-E slot. Then add a discrete card.
One issue could be the PSU though; a high end card may be too taxing for such a system.
Yep. You'll have to dig down into the online specs and manuals to look for PSU wattage...and to see if the PSU has the PEG connectors you need for the card...
...and this goes without saying, YMMV on noise.