Hi and welcome,
If you check this link:
http://www.scan.co.uk/shop/computer-hardware/all/cases/performance-cases you should be able to find a suitable chassis for your PC. If you do not see anything that you like then you need to look for a case that will take an ATX motherboard. The size of case will also depend on the length of the Graphics card as some cases can make things a bit tight in that area.
A thing to remember is that, a smaller case will need to have good cooling to dissipate the heat that is generated from the CPU, GPU and other hardware installed. Overheating is a killer when it comes to PC's.
The basic system you have inherited first came onto the market back in late 2008 early 2009 so it is quite old as far as CPU/motherboard tech goes but, in its day, was something that a lot of users aspired to and was pretty much top of the range. If everything is working fine then it will still be a pretty good PC.
The graphics card is a current model and should handle gaming pretty well.
