I didn't know that brass wool doesn't work with lead free. The folks on our production floor have all switched recently to brass wool from wet sponges, and they use lead free about 95% of the time, with either water soluble or no-clean flux as called for (more WS than NC, but not by a huge margin). I haven't tried brass wool yet, but I guess I'll have to try it soon. If it's not as good, I'll have to berate them for liking an inferior product ;-).
At work we use SAC305, which is SnAgCu, 3.0% Ag, 0.5%Cu, balance Sn. In my own work, I've found that I prefer Sn100C. It produces a nicer finish and I think it wets better. I don't know the exact composition, but it is NOT pure tin. The tiny amounts of additives (which are patented, but I don't think secret) make Sn100C very different from Sn100. Having worked a fair amount with both SAC305 and Sn100C, I'd definitely recommend paying the small premium for Sn100C. I pay more for royalties than for silver, but I don't care. The cost is trivial in the long run.
Of course I would prefer to use 63/37 (it isn't an accident that it's been the most popular alloy for generations), but I ship a lot of stuff out of the US, so I use lead-free for everything, rather than risk cross-contamination. I keep the 63/37 around for personal projects because it's so much nicer to use, but I have a separate iron, sponge, etc, just like we do at work. It's all been in storage for quite a while now.
I have a roll of 0.032", which is great for tinning and for larger joints. For really fine work I have a roll of 0.010" which I love. Most modders won't need it, but if you assemble boards with fine-pitch parts, I highly recommend it.
One thing that hasn't been mentioned so far is that it is really important to keep your tips tinned (coated in solder). This keeps the tips working at optimum performance. When the tip is coated in solder the solder oxidizes, and this is okay because it gets wiped off. When the tip is exposed, the tip oxidizes, and this is bad. Strangely, it seems to be most important when you turn the iron off. I always tin the tip before turning it off, and frequently check a few minutes later to make sure I didn't forget (I'm not as young as I used to be).
Nobody over-emphasizes the importance of flux. It would be hard to do, as flux is really important. Without flux it would be nearly impossible to make good joints by soldering or brazing. In big joints - tinning wires, boards to pills, etc, the flux that's in the solder is often enough (assuming you are using flux-core solder, which almost everyone does). But in small joints (like 0.010" wide pins on 0.019" spacing) it really helps to have liquid flux applied prior to soldering. =