Ok you have three different types of games there:
Bubble Bobble II isn't all that advanced a game. It should run fine on most systems. Nes performance varies greatly by the emulator (don't ask me which is fastest) but you should be able to run it on darn near anything. Sf zero is a cps2 game.... those require some processing power.
Your specs are a tad too vague to understand where the problem is coming from.
for example:
1.6 ghz celeron... what's the bus speed? Is that single, dual or quad? (I'm guessing single)
An internal video card is obvously crap and it's obviously slowing down your system, BUT what resolution are you running mame at? For an internal card especially on a system with so little ram, that will make all the difference in the world. You are probably going to have to run mame at as low a resolution as possible. Make sure "switchres" is turned on and resolution is set to "auto" in your mame.ini.
So to answer your question on what to upgrade, the real answer would be the whole pc.

Joking aside, I don't think you can do it for 40. You really need more ram AND a video card. At least going with the assumption that you aren't running an arcade monitor.