Here's the scanner I was telling you about: https://www.crucial.com/store/systemscanner
One thing to bear in mind if you upgraded the current system with a new graphics card is making sure it would fit the case, as the case looks quite small. Also that the psu would be able to handle it. Assuming I've found the right system on the hp website, the power supply is 310w which is low. Something like a 1050 is on the smaller side, so that might work, and only seems to need a 250w psu, although that might be pushing it. Some sites suggest 300-350w. Maybe a 1030 These cards are an upgrade on the onboard graphics, but still on the lower side as far as playing modern games with decent fps. Might be better just to wait until you were upgrading everything, if you decide to wait.
Could always try an ssd/nvme first and see how much of a difference it makes. Decisions, decisions, haha.