There is no issue with motherboard/gpu compatability, there is a pci-e standard and they are all backwars compatibile. You can take a brand new gpu and put it into a 5 year old motherboard and it will work, or vice versa.
In a desktop PC (assuming you are talking about a builders case and not an OEM like Dell, HP, etc) there are many standars so there is only minor issues with fitment.
Boards come in 3 main sizes (form smallest to largest) ITX, mATX (m is micro), and ATX. Any ATX case will fit any of the boards, but if you get a mATX size case it will not fit a full ATX board.
The other main issue with fitment is GPUs, the more powerfull the GPU the longer the card probably is. You will need to make sure your case is deep enough for...