Unfortunately one part of your PC is well under spec for running the engine, the minimum GPU requirement is a GTX 470, which is at minimum 4 times as fast as the GT 625.
If you want to upgrade, you can do it pretty cheap, or spend more for a faster card. At the lower end, the nVidia GTX 660 or a GTX 750 Ti are good cards. They vary from $150-$180 here in the US. If you want something stronger the GTX 760 is about 30% faster than a 660, it has $250 MSRP; the GTX 760 is the sweet spot for price and performance in the mid-high end market right now, I wouldn’t go above it unless you’re serious about running games on max settings. If you want to spend less you can find a 650 Ti Boost, which is pretty close to the 750 Ti, or maybe a used/refurbished 560 Ti/660/660 Ti. The 560 Ti is about 15% faster than the GTX 470. AMD cards have heavily inflated prices at every retailer in my country right now due to mining, so if you’re on a budget I don’t recommend any of them. The Radeon 270X would be the AMD card to begin with, it should around or a little faster than the 750 Ti.
EDIT: Saw your question about a GPU under $500, which is a pretty high budget. You don’t need to spend that much. A GTX 760 is a good compromise between power and price. If you want to play demanding games on max or near max settings or if you’re serious about doing as much as you can with UE4 you could consider a GTX 770 or a Radeon 290 if you see a cheap one. I wouldn’t go above either of those, the dollar to FPS ratio gets really bad at the high end.