Well, the case itself isn't going to be the issue persay, it will be mostly the Motherboard you will be putting into the system and the Power Supply Unit that is in the case.
Ideally, you can swap out the Power Supply and still keep the case, but it is really the main board that will be your biggest problem with the case. If the case's back panel, for instance where your USBs, ethernet and what not, don't line up with the back panel or you can't remove the back panel, or worse yet, the orientation of the board is not matching up with your case... You are pretty much needing a new case in general.
The only other issue with your case would be how much room there is and what you plan on putting in the computer. If you are looking at a mini-tower or mid-tower, you will have minor to major space issues if you have to put in a large CPU heatsink cooler, possibly some air flow issues. That and it makes it a pain to do upgrades if you have a large hand with regards to memory and such.
Depending on what you plan on doing with the computer and also how quiet you want it to be, you may want to also mention 'how far' you want to go and what you would like.