Yeah, you gonna need a new PSU for sure.
Look for the amperage by the rails, this is the most important part. Different 9800GTX+ production companies may have different minimum psu requirements, but I'm going to take a stab and say that it's probably 24A-30A minimum, again depending on brand and clock speeds.
Note that the wattage on a PSU doesn't really mean anything. It can be really high 500W but still only have like 22A on the rail.
I have an 8800GTS (the G92 512mb ver) , and mine is at 24A. The G92 8800GTS 512mb should be neck to neck with a 9800GTX+, marginal difference if compared by the human eye, we're talking like 1-5 fps difference per a game.
I haven't been playing games for awhile, but I have crysis installed. If you want me to do some FPS benchmarking for you I can do that, at what settings you would like.
I think I run at 1920x1200 at very high quality but no AF enabled. About 2x or 4x AA, I forgot which. The game is really smooth, don't remember any lag except if I am fighting like 30 soldiers at once
It is hard to recommend what card for you since I don't know your gaming style. But if you want to see general FPS charts, I use the ones at toms to get a general look at rankings:
Charts, benchmarks Gaming Graphics Charts Q3/2008, Sum of FPS Benchmarks Totals
Are you looking to buy right away or get a good deal? If you are looking to get a deal, a great 9800GTX deal just passed a few weeks ago.. it was for $98 shipped
EVGA GeForce 9800 GTX+ 512MB GDDR3 PCI Express x16 (2.0v) Video Card $95 after $30 MIR - SlickDeals.net Forums
I was thinking about getting it but I decided not to, since it would just be waste of money for me. But for you, from 8600 > 9800GTX+ you will notice a big boost and can set your resolution to 1680x1050 with decent settings fine. If you can wait, the market price for a 9800GTX+ is around ~$130 now, and sometimes deals come out for $100 or so after rebate.
Also about your case. Kind of hard to tell without actually seeing it in real life. I am guessing if that is the standard case size, it should fit inside fine. It doesn't have a front bay fan or speaker so you have a lot of legroom.
Personal advice, wait for the 200 series to fall in price. Right now the 9800's are falling, but the 200 is still kind of new so it is up there. The difference in price per performance ratio is very high.. you are paying like $100-200 more just for maybe 10%-15% improvement. That is like 10 fps - 15fps improvement. It is your own choice, but is 10fps worth $100+ to you?