Need a New GPU

[nuuskupe]

I've a computer with specs displayed below, and would like to upgrade my graphics card to a better one. What graphics card would suit my system? I'd preferably want something i could run games with decently.

I'm fully aware that i would probably require to upgrade my PC before getting a new Graphics Card.
If so, what steps should i take?
I've already asked here about a new PSU for my rig and think I could upgrade to a 350W one, but don't want to if there are other options.

Current Specs
Motherboard: Acer Aspire X3960
CPU: Intel i5-2300 (2.8-3.1Ghz)
PSU: Lite-On PE-5221-08AF (220W)
Graphics card: Nvidia Geforce Gt420 (Yuck, it sucks)
RAM Memory: 3x 4GB DDR3 Modules (Adds up to 12GB)
Hard Drive: 1TB

Any help appreciated.

 

[clutchc]

I believe that PC has a small proprietary PSU. Not going to find a replacement that would fit or match connectors. The best I'd try with that PSU would be a GT 1030. I'm afraid the GTX 1050 or 1050 Ti would be too much for it.

The GT 1030 should give to a huge boost in performance over the GT 420.
Here is another comparison.