What is graphics card would best suit my PC

I have been using an integrated family graphics card for a long time, and now its time to for an upgrade. A while back the problem with my PC is that it is a slim/half size PC, meaning that regular graphics cards will not fit in the case. What sort of graphics card do I need? Or is it best getting a new case all together, thanks.
PC Specification:
Operating system: Windows 7
Manufacturer: Lenovo
Model: Lenovo H330 Slim desktop PC
Current GPU: Intel (HD) Graphics family (1696MB)
Processor: Intel(R) Core(TM) i5-2320 @ 3.00GHz
Installed Memory: 4.00 (RAM)
 
I vote for a new case.

Any half-height card available would not be much of an upgrade. And any upgrade might also put too big a strain on the power supply. And being a low-profile case, the PSU will likely be non-upgradeable.
 
I vote for a new case.

Any half-height card available would not be much of an upgrade. And any upgrade might also put too big a strain on the power supply. And being a low-profile case, the PSU will likely be non-upgradeable.

Yeah I was thinking that aswell, but im not that experienced when it comes to installing hardware and stuff, dont wanna break it haha.
 
It could be a challenge. Check the power supply to see how many watts it has. Fitting a new psu would be tricky firstly because it is probably an unusual size and secondly I reckon that you will have to remove just about everything from the case first including the motherboard. Moving everything to a new case would work but ask yourself if it's worth all the trouble. The H330 is doing what it was designed for.
 
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