4.3.1 is the latest for an untethered jailbreak (no need to be hooked up via USB to a computer to reboot). Redsn0w will work if you don't care about updating your baseband.
Essential Cydia apps/tweaks?
SBSettings
Springtomize ($)
iFile
My3G ($)
TetherMe ($)
It really depends on what your needs are though. There are a few threads on the best apps/tweaks in the iPhone Hacks forum.