Intel I5 2.4ghz, 4GB Ram, GeForce 770 which I picked up used because I thought I would be running more powerful games.
2.4Ghz is way too slow if you plan to "be running more powerful games" in MAME
For 3D games in MAME, your processor has to emulate both the original processor and GPU.
Your graphics card doesn't help at all.
It takes more like 3.5-4Ghz to get games like NFL Blitz and Ridge Racer playable.
The graphics card is important for Demul and other emulators that actually utilize it.
If you were referring to more powerful PC games and aren't worried about the 3D games in MAME, then it should be fine.
MAME uses OpenGL which WILL be processed by the graphics card. The i5 stated plus a decent GPU will be fine.
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The video card is used for post-processing effects only, not the emulation.
The i5 is a decent processor, but won't run everything.
*nothing* will run everything, there's no processor on the market that will run Naomi stuff (Marvel vs Capcom 2 etc.) at full speed in MAME, although there are certainly games that a faster processor could run that the i5 won't.
I imagine in busier scenes some of the Cave SH3 shooters will drop frames on the i5 for example (I tried a lower clocked i5 a while back and they did, although i5 does cover a wide range of processors, some much better than others)
Of course, it's up to you if you want to run things like that anyway, some argue that without the slowdown of the original games (that for very complex reasons, isn't accurately emulated yet) the games are too difficult to play anyway as so much is happening so quickly you don't stand a chance.
Golden Tee Fore! series will definitely drop frames on the i5, even on a 4ghz i7 you have to set it to the lower resolution to ensure it never drops frames (otherwise some busy woodland areas can dip to 80% if you take a really bad shot and end up in 50 trees) Of course, Golden Tee Fore! requires special controls (trackball etc.) so isn't really suited to most cabinets anyway.
From what I've heard, in terms of space, it's a lot of the extra (videos etc. for frontends) that end up taking the majority of your space up rather than the actual roms.