The main things Im needing are:
Some sort of word processor, PDF creation is a bonus but not required
Unfortunately there aren't good native word processors yet (Papyrys wasn't that good apparently), but good old word processors from Amiga do work fine. At least Pagestream can save to PDF.
Web browsing obviously
MorphOS version of OWB is really good, but also IBrowse and other old Amiga browsers work fine if you're used to them and want to experince some real speed

some sort of chat client, preferably including MSN, AIM and gchat, if possible
There are some programs for those... but I can't remember the names just now. IRC FTW

AmIRC (there's MorphOS native version with some fixes since 68k versions) and WookieChat are good IRC clients.
MP3 player. Bonus points if it can play .ogg and mod files as well
AmiNetRadio for the modern bloat (plays lots of formats including mp3, ogg, mod, ahx, hvl etc) and SongPlayer, AMPlifier, AmigaAMP etc for traditional mp3/ogg playing. UADE for precise mod and other Amiga format playing.
UAE in some form or fashion 
There's E-UAE ports and MorphOS runs system friendly 68k software transparently with its own Trance emulator.
If there's a decent graphics / paint program thats a bonus (and if all else fails, there's Deluxe Paint 4 in UAE I guess)
MorphOS has ShowGirls, which is excellent image viewer and processor. It's especially designed to process digital photos. MorphOS also includes Sketch, which is basic, but pretty modern painting program.
Most of the Amiga's graphic programs work too. I keep using ArtEffect, PPaint and FXPaint2 regularly, but for example ImageFX, Photogenics, Elastic/Fantastic Dreams and TV-Paint do work too.
You can check
MorphOS 2 review for more detailed information about the system and included programs