for an A2000, the best you can get is OS3.9, and if you can, get the netconnect 3 bundle. has the full registered voyager built in plus loads of other goodies. i used to use an A4000/030 16Mb with netconnect 2 for internet stuffs just fine. but the more memory and disk space, the better. really, an 030 is just about acceptable as a web browser. and 4Mb of fast is the absolute minimum for the web, i wouldn't want to get by wioth less than 16Mb if i had a GFX card aswell.
if you can, get an 040 or 060 card, and lots and lots of ram. (ok you don't need it all the time, but its nice to have it there for the occasional time you do need it.)
A cybervision64, CV3D or PicassoIV would be good as although they are dated by todays standards, it'll be an improvment over your picassoII (smoother screens, more colours for rendering web pages etc.)
OS4 is PPC only, and there is no viable PPC option for the A2000, unless you used to work for phase5 and have one of the dev boards that can drop into an 040/060 socket of a blizzard 2040/2060. :-) (warpOS has a hardware application layer in the distribution to support the development boards)
other than that, its either a A1200, A4000, A1 or derivative PPC for OS4.
the choice, as they say, is yours.
BTW if you are going for a PPC card, i'd go for amibench. people there are much more genuine