The A3000 will be fine with the ethernet board. You probably won't get the 300-400kb/s you would if it had an 060, but using AmiTCP/Genesis you'll probably get up to 100kb/s.
If you use something with low overheads like FTP, it'll be quick, but obviously a *lot* more sluggish if you want to run a Samba server which is a bit resource hungry.
Web transfers will obviously be faster so long as you're not waiting on the browser to display images, draw the HTML page, etc.
@Ali
If you want an ethernet board, I might be able to strike you up a deal. Got at least one spare.