Which PlayStation 1 emulators would you recommend?
I'm somewhat of an advanced user, but still would prefer one that can be fired up quickly without too much tinkering (leaving the tinkering for later time).

visit this

ePSXe,
but you have to play a lot with plugins. (Not sure what your knowledge of emulation is)

Easiest is VGS (Virtual Game Station), but it has also limited options and is not supported for a long time (it was commercial product, till SONY purchased it, and company that sold it is now part of MS empire. (Connectix)

http://www.ngemu.com/psx/index.php

Go there they are the official site of most of the PSX emulators, also check out the forums if you need help...
I'd definetly recommend you epsxe, following by PCSX, PSXeven. VGS and Bleem are the most simple emulators, but lack compatibility so except if you're a total n00b at PCs(which methinks you're not), you should avoid them...
For plugins, anything with Pete's name in them is great...

I second that.

Thanks for reccomendations, will try them.
As for the plugins... I guess I'll figure everything out.

That's the best way. Try and error. SOme games work best with some plugins. Also you should have a nice PC to emulate at fine speed.

And did we mentioned BIOS, that you need, and we can't point to them, as they are protected by SONY. (Hint: VGS does not require BIOS ;))

PCSX doesn't require BIOS either but I doubt that you'll be able to run anything with it though...
Ok I'll edit that, but that's known information it's in Epsxe FAQ...

Tulac, you should not tell him that, he should be smart enough to do it on his own. (you better edit that post, before some moderator edits it, or someone reports it to moderators)

Requirement of a BIOS image was a little unexpected, but now I've got it. Thanks for advice, all.