OK man, here is the best thing you can do....read stickies and use the search button. All your questions will be answered. But i will go ahead and answer your questions cause im bored...
OK motherboard, it doesn't matter what motherboard you get anymore, TA-82's are downgradable, and yes there is more than just those two.
Firmware...go to my thread on determining firmware version from the box of the PSP...
http://www.pspmod.com/forums/showthread.php?t=17346 (How to play onlie)
Just go to walmart of whatever and check the box, i would recommend getting 2.71 or lower if possible, cause 2.71 is the best and easiest downgrader at the moment...
The latest firmware out is 3.40 made by sony. What you are reading about 3.40OE-A is not made by sony, psp hacker/programmer Dark_Alex made that firmware. It looks and operates just like Sony's version just allows you to play backup games(ISO/CSO), play homebrew, emulators(playing NES, SNES, Sega, N64) on your PSP, and loads of other awesome features. In order to get to these firmwares you HAVE to downgrade your PSP to version 1.5, don't ask me why, that's just how it goes, hence the reason we downgrade to 1.5. Once at version 1.5 then you can Re-Upgrade to 3.40OE-A and start doing whatever modding u would like.
ISO/CSO are images of a UMD(PSP Game) which are ripped from a umd disk just like ripping a CD with music, the purpose of doing this is to eliminate the carrying of UMDs and depending on the size of your mem stick u can hold multiple games on it.
Hope this answers all your questions bro...if you got anymore just use the search button, it works wonders...
EDIT: By the way i forgot to mention this, if you get a PSP with higher firmware than 3.03 or you decide to upgrade, u will be ****ed, just a forwarn, if you want to get into modding don't buy a psp that has firmware higher than 3.03...