Wished I would have painted mine - the hat is the area from where the rotor meets the wheel over to where the caliper meets the rotor. All this area will quickly get surface rust growing on it...not pretty. See mine in the attached photo. Hard to really see, but it's the dark area behind the rim (you can also see the rusty color on the front edge). (Now you can probably understand why they call it a hat as it's hat shaped! ) Best of luck! PS - be sure to use liquid pipe thread (as opposed to teflon tape) to seal your lines. PS2 - make sure you have the proper flare wrench.
I didn't paint mine though have such a dark thick coating of rust/brake dust it might as well be black paint. Even with my FR500s on I don't notice it, because the rust is so dark it gets lost in the shadows. I imagine it depends where you live, if you live in the rust belt and they are going to get dark thick rust I wouldn't bother. If you live somewhere warm and sunny where you'll get mild brown rust I'd do something about it.
A flare wrench is specially made for a flair nut (suprised? LOL)
It wraps 3/4 of the way around the brass (SOFT!) flair nut and prevents rounding - believe me, you don't want to round these off and have to replace em.
I bought a set of 3 flare wrenches at Advanced Auto Parts for about $7-8 bucks...well worth it. (Especially as you have to tighten these nuts pretty well, they get wet with brake fluid (which is slippery) and if they aren't tightened, they'll leak (been there, done that)). Other than a bit of a leak on the pass side, this install (and bleeding process) was simple and straightforward.
I used this writeup as a guide --> http://www.fordmuscle.com/archives/2005/02/BigBrakes/index.php