@Computerilleter, welcome to the forum.
The problem that you will have is the fact that the power supply unit (PSU) in the computer is only 180W. I suggest that you get a PSU with at least 500W. You should choose a PSU that you like and get the measurements of it. Then, measure the space where the PSU will be installed to ensure that it will fit. I like Corsair products. Also, modular PSU's are better for small cases. You only use the cables that you absolutely need.
If you upgrade the PSU, here is a video card that will give you good performance. It will definitely fit into your case. Read the Customer Reviews to see what users have to say about it.
Please click the Thumbs up + button if I have helped you and click Accept as Solution if your problem is solved.

I am not an HP Employee!!Intelligence is God given. Wisdom is the sum of our mistakes!!