Not sure about the psx emulator. It's been a long time since I messed with one (don't care for many psx games).
Last time I ran one it was using an old Nvidia 8600GT and it worked fine.
It wouldn't surprise me if onboard graphics could handle PS1 emulation.
If you're talking about emulating PS2, that's a whole other ballgame.
With MAME, it's a case of diminishing returns.
You can play 2,000 games with an abandoned piece of crap found next to the dumpster.
Or you can spend $300 and play a couple dozen more, or spend $800 to play a half dozen extra on top of that.

It just depends on where you draw the line and what being able to play three or four more 3D games is worth to you.
If you like the newer 3D games, I recommend the fastest i3 or i5 you can afford and a 50ti or 60 series NVidia card (460,760,860,750ti).
The Sega Naomi games on Demul emulator get as much play as MAME on my cab. (I'm actually running them on Makaron emulator since my PC is outdated, but it's one of those old PITA emulators that info is scarce on)
So outdated it's not relevant, but I'm running a 3.4Ghz Athlon X3, MAME v.146 & a 750ti (upgraded video card so I could play Mortal Kombat X).
It runs Tekken 3 with occasional sound skips with HLSL disabled and no scaling. I tried MAME v.170 and it choked hard on Tekken and all the late 90's 3D shmups.
It won't run the Naomi shmups in Demul without horrible slowdowns, but it will run them with an old emulator called Makaron.
So I'm not recommending my hardware, but there it is as a point of reference.
It also demonstrates how dozens of games will run full speed in an older version of MAME, but be completely unplayable in newer versions because of MAME becoming so much more demanding.