First off.. dont let it bother you so much (not saying it is bothering you, but just be mindful not to get worried) If you worry, you dont relax, and if you dont relax, you do poorly. There are lots of good drivers who worry about the rain and let it beat them, not their competitors.
The biggest things are a different feel, and then a "rain line"
The feel is to remember that you are not going to be pushing G limits like you are used to, so that seat of the pants feel goes away a bit. Continue to relax, and like you said work your way into the speed and remember that now, like in autocrossing speed becomes realitive and you have to "slow down to go faster".
The next, and probably most important is the "rain line" the dry line on a racetrack gets polished smooth, and makes for hell when it rains. THe general rule is to cross the dry racing line while going straight, and stay out of the normal line in corners. Tight corners you usually end up taking on the outside, long corners you usually end up taking on an inside line.
But.. the real key is just to look for where there is grip, stay out of deep puddles, and find the spots where the car grips.
Have fun, racing/driving in the rain is a blast, if it were up to me i would install sprinkler systems on the sides of all the racetracks.