I have a Phat, too, currently running PSPGEN 5.50-D3. Unfortunately, the older M33 custom firmware hasn't been updated in quite a while, and won't work with the Playstation Network games. PSPGEN is in current development, and does.
As to flashing, I can't quite remember the order you need to do it. However, I discovered an excellent tutorial:
http://forums.pspslimhacks.com/tutorials/2179-tutorial-how-install-cfw-any-psp.html
VERY nice! Since you have a Pandora battery, and a 2 GB memory stick, you should be fine. Your 1000 model is completely hackable, and the default PSP GEN install should do most of what you want - although some homebrew won't run without earlier firmware modes installed.... I don't recall how you're supposed to get the 1.5 and 3.7 support running in the later versions, but I'm sure you can find it.
Make sure to update PSPGEN in order! See the tutorial :D