Ignore the posts above, you don't need a Pandora battery. Go here:
PlayStation Guide
OFW 6.60 Download
CFW 6.60 PRO-C2 Download
You will see 4 CFW options to choose from. Pick the bottom right one '6.60 PRO-C2' (this is what I use, and I'd highly recommend it), '6.60 ME-2.3' has a few quirks. Don't bother with 6.61 either as there are a few plugins that don't work with it, and no games need it.
Make sure you follow the steps on that page precisely for installing. The first thing you should do is install OFW 6.60, then CFW 6.60 PRO-C2. After you have installed CFW, every time the PSP has been fully powered off, it will boot in OFW mode, you have to run 'Fast Recovery' to switch to CFW mode, so I'd then recommend making the firmware permanent by running the 'CIPL-Flasher Tool' (Note: Only use the 'CIPL-Flasher Tool' after you have installed CFW '6.60 PRO-C2', not before).
All these steps are reversible (even the permanent patch) if you ever want to put the PSP back as it was (although '6.60 ME-2.3' is a pain to uninstall, '6.60 PRO-C2' is easy to reverse).
With regards to your memory card question, I use a Micro SD to PRO DUO Memory Stick Adapter. They are £1.75 delivered on Ebay (or 99p from China). I use a 64gb Micro SD in mine and it works fine.