Here's my $.03 (inflation, you know) as I've tried several since getting mine.
I dumped the Sharp rom right away and went for pdaxrom. Nice, but the screen flicker was annoying, and well, it felt kind of slow. It also seemed like battery drain was a little higher than it ought to be, and that combined with it not liking my wifi card (Ambicom) and other little things, I dumped it and went to...
OpenZaurus 3.5.1. I think I liked this a little more, even though I really wanted to like pdaxrom because the idea of having a full little X system really appealed to me. I ended up wiping and reinstalling OZ after having some problems with various packages (user error). I was able to get most everything I wanted installed on it, but when I tried to load weather.com and it took30 seconds with Opera, and my ipaq can do it faster, I got a little miffed. And then I couldn't get TextMaker or some emulators to work, so I wiped that in favor of...
Cacko rom. I have the hotfix installed now, so version 1.21b, I believe. This is based on the Sharp rom, and of all that I've used now (I did briefly use the Sharp rom before dumping it, I have to admit), I like this best. It just looks professional and very polished. It also seems faster than the other roms I've used. Netfront is pretty fast, as is Opera. It could be that I was using Opera 6 before and that Opera 7 (7.3?) is better optimized, but there's a noticeable difference. I've also managed to get everything to work on the first try, but I haven't installed kismet or Wellenreiter yet. They'll be the real test for me.
Right now, I'm really enjoying cacko, and I'm looking forward to the next version. I've had no stability issues with it, whereas I managed to completely freeze pdaxrom and OZ more than once (again, probably more user than system fault). This isn't to say that pdaxrom or OZ aren't good, not at all, just that my current preference is cacko. I still intend to try pdaxrom when the next version comes out (preferably not an RC).
I think any rom will be able to do the core of what you've asked (aside from java, as Chaos noted), so it almost comes down to style and whether you want X or QT, or both, I suppose.