The cards I recommended are quite small, would just take a little measuring of the inside of your case and checking the dimensions of the GPU from the manufacturer.
There is no guarantee that newer cards will work in older systems, particularly OEM machines. I've often found that the vendor's forums will often have success/fails posted by end users who have already tried. I'm quite certain the 900 series and up from Nvidia have a somewhat unreliable history with backwards compatibility. Some would only work once the OS was running for example, meaning it was next to impossible to build a new system with a new card and older parts. All comes down to the switch from the old style BIOS to UEFI.
AMD has a better backwards compatibility success rate from what I have seen, but there are no real guarantees when you go back too far. OEMs tend to not make many BIOS releases for the motherboards they sell, so while you would find more support from one of the board vendors, you won't see as much from Dell/HP etc.