I just use an old 25W soldering iron, I know it's probably a tad hot for doing modchip installs, but I've never had a problem. I've done original Playstations, Dreamcasts, heaps of Xboxes, a couple PS2's and a couple of Neogeo AES's.
The tip I use is just an old tip that I stuck on the grinder to make a very fine point in order to do the PS2's.
I'll have to get a new iron one of these days
But yeah, take your time with your PS2, it's not as easy as it looks, especially for novices.