You don't need to worry about the PSP model or FW version anymore. Apparently the "jigkick" method will work on any PSP, though I'm pretty sure you will need someone who has a hacked PSP to set up everything for you. I know pspupdates is disliked around here (for valid reasons) but you can find more info about this
here. Use noscript though because that site is bogged down with tons of shit.
Edit: There's also a way to play PS1 games legitimately by buying them through the PSN store or whatever, but I'm pretty sure you need a PS3 to do so, and I don't think the selection is all that great. Anyway, I don't know why you would pay for games you already own. It's not piracy if they already have your money.
Ya, I've downgraded a few now using my Pandora's Battery and a 64MB "magic" memory pro duo card. It's an easy enough process going down from any firmware (even 3.71) to 1.50 and back up again (I go 3.40OE to 3.52MM-4 right now, but I'm going to start using 3.71MM after the next patch comes out). Anyway, you have to use the battery and custom memory card to re-write the firmware directly to 3.60MM if you have a PSP slim, though, and that requires a little more set up. Either way, you have to prep the Pandora's battery and the firmware updates on a PSP that's already running open firmware, so unless you know someone or can find the el-cheapo "mod" services in your local on-line classifieds, you're going to need to use a more conventional method of getting an OE firmware on your system from the first - and I believe that requires a PSP phat with a firmware not higher than 3.50 (but I could be wrong about that - I'm not keeping up since the Pandora's battery makes all that irrelevant to me)...
PSX emulation on the PSP is fantastic - I've played through all three PSX Final Fantasy's, Metal Gear Solid, Silent Hill, R-Type Delta, and a few other titles on my PSPs - I love it!