I personally go with Nvidia for my GPU's and I always have a rule of never buying a card under the x60 series, generally Nvidia cards have a huge drop off from the 60's to the 50's, the 50 series tend to be their highest priced cards that still target the standard user types who buy PC's at Walmart and need a video card to play The Sims and such but nothing overly cutting edge. The 60 series on the other hand is the entry level card that is aimed at the enthusiast gamer crowd and is usually a much larger step up than say the step up from 30-40 or 40-50. This has seemed to be the overall pattern and strategy they have been using for many years now. I would highly recommend you go with at least a GTX 660, with the 760, 660 Ti, and 760 Ti being the ordered next stages of better cards you could go with. Price for performance and longevity between upgrading again as well as matching your overall system a 750 would just be letting you down.
I run a R7 260X. Although it is not an Nvidia fanboy (like me)'s dream to own an AMD card, it is pretty decent. A 750 Ti is also not out of the question, though. Get a 4-core or higher AMD CPU or a Core i5-higher CPU to go along with a new GPU for Beam. You will desperately need it.
Yes, you'll have a blast playing this game with that hardware. I have an i7 920 @ 3.43Ghz and a GTX 260 and I run on high with plenty of frames to spare on any given level. Until the Core series maybe....after that, not so much.
at high settings, i would say 720p. With normal and some things set low like i run at, you can expect upper 50's at 1080p.
I don't know, man, look at this, http://www.anandtech.com/bench/product/1129?vs=1079 That's a comparison of the 650 TI and my GPU ( Radeon 7770 ) and they seem to be pretty even although the 650 performs a little better in some games. In BeamNG Drive with everything on high - except lighting, which I have at normal - at 720p, I get 50 - 60 FPS and that's with anistropic filtering at 16x and anti aliasing at 4x. If I set lighting to high though, I lose about 15 - 20 FPS.
To put things into perspective for you a little if you haven't bought a GPU yet. I've got an i5 4670K at the stock clock and a GTX770 with a small OC from Gigabyte and I pull off 95-110fps with everything on high. A GPU should be the most expensive part of the build
I have a GTX 650Ti SSC. and I push around 50-60fps. That card is a good card for almost any game, maybe not max or high, but medium setting.