Ok, my little story..
I've been a miggy user ever since when... a silent lurker in these forums but always hands-on active.
Left for a while because of personal things but got the Amiga bug again (again..again) about a year ago.
Decided to trick up my A2k (see avatar) and have enjoyed countless gaming/demo sessions on it. However, I got bored with seeing 'requires AGA' or 'not enough memory' when trying things on my (somewhat vast) collection of cover CD's. Especially demos! Not happy with this, a choice arose. Upgrade my A1200 or replace the A4k I sold years ago (regrets!)
Much money later, I now have (in order of purchase)-
Amiga 4000 in Micronik tower (the one with the front door) + bus board
4GB CF HDD
A3640@33mhz
3.1 Roms
Cybervision 64/3D
Now that I'm enjoying all of these colours and pixels I'm wondering what more I am missing and what more this machine has to give.
Now my question to you good people is where should I go from here?
Please bear in mind that I'm under no illusions of going on the Net with it but, really do enjoy demos and gaming.
Your suggestions are welcomed 
...you have a bit of an odd kit, for a demos / AGA project. It is a partially tricked out machine, relegated to not much.
You toss in an ethernet board and you could get on the web - pages wouldn't display flash content and there is no java, but you could definitely do basic browsing and send/receive emails. I am guessing YAM is still around, if not something newer and better.
Upgrade to 060/ppc and you have a nifty little email/mp3/game machine, though a pricey one. The A3640 doesn't have local ram, so that bottlenecks you a bit. A better accelerator with local memory would speed things up nicely (though kudos on the overclock, that helps a LOT on that board). If you can find one, a Blizzard PPC would open up PPC demos to you, as well as OS4 (I think?). With OS4 you can step up to webkit and Mozilla based web browsers. I guess it all depends on what you want to spend on your bug.
My last tricked-out miggy was an A4000 desktop with 060/50+PPC+CVPPC. I had to sell it after the terror attacks of 9/11 caused my company to go under...I lost my company car and had to buy a car to find work. Presto-chango - The Amiga turned into an old, used Chevy Blazer. I later sold my stock A1200, as I didn't foresee having the cash to upgrade it to a usable state. I would *love* to have an Amiga again - but I can't justify spending the money when I can get so much more power for so much less dough. I guess I am more practical than I once was - not to mention the pocketbook is smaller than pre-9/11.