Is the 2320 flicker fixer something I can use with Picasso 96, or do I have to get something else? (I ask this question because I already went through the Green Amiga Alien Guide on my emulator as a dry run).
If I understand your question, your Flicker Fixer/Scan Doubler is purely a hardware solution to convert from Amiga native 15kHz video (Television) to 31kHz video (VGA type). The screen resolutions that were always available in ECS will still be the norm, the interlaced modes will simply be much easier on your eyes.

No software or drivers should be required.
Your 2000 is nicely equipped for most Amiga apps. It can do many things on the net (email, etc) as is. Many people would rather have a retargetable graphics card (this will require P96 or similar) for surfing, although, there are screen shots here of folks surfing with ECS (Mr.a500, etc). Also, many would like a more modern browser than is available currently (iBrowse).
Did you catch some of the recent threads about updating OS3.1?
Oops - someone beat me to it.