What GPU cards will run Windows 10 64bit?         

First off  all new cards sold do this,  but watch out or dirt bags,  selling old cards as new or China Counterfeits (endless) . (Do not buy old cards from SCALPERS)

If the  W10  loaded PC shows in device manager  under DISPLAY ADAPTERS as  MBDA  driver, this means a lame and  weak basic limphome
driver, from Microsoft (MS) 
If you have and old PC most  old Intel HD chips (GPU) have no driver support at all now. ZERO or ended at XP ,to W8.  End of the line.
Then you get the idea gee a newer GPU card that supports W10.
The given #1 is the Intel iGPU is now not supported, and you need 3D Graphics to work on W10.

There are only 2 chip makers for cards today and support, but best is look here for both chip makers drivers.  Your OEM PC maker already told you NO. (given #2)

NVIDIA.com  ( series 7 and up are supported )
That means GT705 is the most cheap card, you pay for speed, buy the card number higher for a faster card.
(learn that better cards even old are expensive due to Gaming demands)

and AMD.com (ATI) Radeon™ etc..  There list here is SUPER GOOD , just one page, all you need to know buying used cards, and wanting W10 support.

The winner for low cost GPU card that runs W10 and directx-11,  is HD 5450 (DVI , avoid DMS59 version)  at the eyepoping cost of $8
The 5450 does a whopping  5FPS, it is a slug but again is only $8 card.  This is only a starting point, so mow 10 lawns and upgrade to faster cards in this list.

There are 12 makers of card now, but all use the above 2 chips, and if the chip maker does not support the chip neither will the card maker nor the OEM PC maker. (captain obvious? IDK)

There is your answer simple and sweet, which one goes fast enough for you is any ones guess. (to get high FPS gaming , only lots of cash is a cure)

But the ratings are HERE . I have a  GTX1650 and love mine, (runs top games too, AAA+)

Finding one that fits and not hit things inside, and not overloading  the PSU , is a whole other matter.

Nothing is more complex as this, and more personal, to go to newegg.com and click the filters there until you get it right is my advice. (only YOU know what you need for ports and speed or Directx 12 needs? )
Learn too that there are older cards the some makers have a  free Direct12 upgrade. (talk you card makers for these facts and there are 12 makers)

My page  rating meter varies by unknown factors. (bovine flatulence?)

Advice, buy  new cards from Bestbuy a real brick store, if no stores in your town go to newegg.com  they do fast exchanges and have the best side bar filters on earth (use the filters, if nothing else, 100% free)

DirectX support page for top CARDs
Nvidia shows GT730 lowest card with Directx 12.

version 1.  1-20-2020