New HTPC, old graphics card?

Hi friends! I'm going to build a new HTPC focused on emulation. I know that the question might be silly but I feel like it's worth a shot. 

I have a GTX 1050ti mini 4gb laying around. Would it be worth it to pair it with a nice and powerful CPU (maybe one of the top tier list) or I'd better buy a new GPU?

I'm talking about running rpcs3 at native resolution and no upscaling.

My laptop has an i5 11400h and a rtx3050 mobile 4gb and I can play ally games at a decent speed. Just to make an example.

In case....which GPU (low profile single slot would be awesome) and CPU should I pick to keep the budget low and achieve a constant 60fps result?

If only want to run games at native resolution (or alternatively FullHD) you don't need a very fast card. The 1050Ti has 4GB RAM and supports Vulkan so you should be good. The CPU is much more important.