TL;DR - This one: MSI GT1030 2Gb with a low-profile, 2-slot, passive cooler, DisplayPort + HDMI output -
MSI site - should cost you ~£105.
Long version:
Decide what cabling you want (i.e. what resolutions you're after, therefore do you need DP + HDMI).... I only point this out as a lot of these are HTPC-focussed and will only have HDMI+DVI or possibly HDMI+VGA!
Technically you could get away with a Radeon R5 (230/235).... it'll be v cheap, but driver support is gone... similarly cheap, but there are GT710 and GT730 solutions out there, but also getting very tired and probably only another year or two of driver support and outputs tend to be limited. e.g.
GT710/GT730 (careful about output options!) the only thing in their favour is even lower price as ~25W TDP.
In terms of what I'd enthusiastically recommend:
GT1030 should do the job nicely.... probably the best option for you and there are a few low profile, 2-slot passive cooling versions of each of those by Palit, ASUS and MSI, but they're slightly more "specialist" items and unlikely to be stocked at OC - forum rules that we can't recommend where to buy them, even if OC is unlikely to ever stock what you're after. 30W TDP (worth noting as this will determine the extra load on your PSU AND the likely extra heat in the case) e.g.
Palit KalmX (great cooling solution, but DVI+HDMI only!) or much better outputs from the MSI version I mentioned at the top (
MSI site ) as that does HDMI+DP! Don't worry about the cooling on these - you could probably just unplug the fan on one of the fan-cooled ones, they generate THAT little heat!
or
GTX1050Ti (75W TDP) if you really want to push the boat out... it's probably overkill for your needs, but the 4Gb version is a genuine 1080P gamer and the GPU is over twice as fast the GT1030 or indeed an Xbox One S (not that that's saying much!).e.g. Palit KalmX
GTX1050Ti
or
GTX1650 (75W TDP) seems like even more overkill than the GTX1050Ti (very similar specs, but it is at least 20% faster) - but look out for it as it is priced very close to the 4Gb GTX1050Ti and will play most games at 1080P with the detail cranked reasonably high!
GTX1650 (same 75W TDP as the GTX1050Ti, three modern digital outputs: dual DP 1.4 and HDMI 2.0)
2 years ago, the GT1030's were £60-£70 and the GTX1050Ti's were £100 for the 2Gb and £120-£150 for the 4Gb versions - I'm not sure what the release price for the GTX1650 was, but the GTX1650super was $160.... expect to pay at least 50% more than that for all of those: £100-£110 for the GT1030 and £200-£240 for the 4Gb GTX1050Ti or GTX1650.
