how to play different console game on ppsspp?

[TheDax]

GBA: Yes, use one of the various gPSP versions.
PS1: No, PPSSPP won't support PS1-PSP games.
PS2: No, the PSP was way too slow to ever have a hope of emulating PS2, so PPSSPP won't, either.
Nintendo DS: There's a homebrew DS emulator for PSP but it's so slow and beta-esque that it's not worth your time.

Also, PSX and PS1 both are and aren't the same console. I believe Sony used PSX for a while as its abbreviation for the PS1, until they then released the PSX, which is a PS2/DVR combo console.

In the long run though, just use Retroarch or other various emulators for NES, GBA, etc. You'll get better performance out of native emulators rather than trying to run an emulator in an emulator (which is usually a Bad Idea™).