time to chime in:
No one has been speaking much to the specs of the PC you want to build. If you're going to go with a machine for "older" games, and just HD video type stuff, you might consider avoiding a discrete graphics solution at first anyway.
If I were in your shoes, I'd save some money, and go with an AMD APU solution. These are usually very compact anyway, and it just might get you the performance you want for MAME and stuff.
Now, I can't say how well it would play Street Fighter 4, but I'm actually pretty sure that it sill at least play it. In my opinion, for a non-gaming (other than retro) HTPC build, an AMD APU is hands down the best bang for the buck.
Again, if you're not hardcore gaming, then 4gb of RAM is enough (especially if you're going to run a boot SSD) With RAM prices super low, you can probably get 8gb for cheap too, but on a budget, in a pinch, 4 will work fine.
Really, that's it. Other than picking out a slim case and a power supply, you just need to worry about how you're going to get everything to work together. A discrete GPU can be added later on if you need to. If you go with a slim case design, you have to be mindful of the type of GPU's you can get that are slim design. (You aren't going to be putting a GTX 670 in a slim case)
My current setup is an AMD Athlon X2, with 4gb of the slowest cheapest RAM I could find in a dumpster. (DDR2) A slow ass mechanical HDD with a 40gb capacity, and a GTX 520. With this setup, I can stream and play 1080p no problem (over the network or Blu-Ray). I can play emulators up to PS2 with smooth graphics (no Dolphin) and 95% of the MAME games work perfectly, with the exception of games like SCUD Race that don't run well on any machine. NAOMI and CPS1, 2, and 3 games run smooth as well.
Here is a quick link to the case that I used:
http://www.newegg.com/Product/Product.a ... 6811154087
It's not super fancy, but it gets the job done, and didn't cost much. The black and silver matches the rest of my gear as well.
If you're interested, I'll spec you out some parts really quick if you're looking to build this yourself. Let me know what you think? The only thing I see coming up as a road block is the difference between US and EU money.
