I use a sheet of glass at an angle over an extra photo tray to help me squeegie off the water as prints come out of the rinse. First I do the back, then lift the print and while holding it up, run the squeegie down the empty glass to clean it. Then the print goes down on the glass face up and I squeegie (lightly) again. Don't worry about getting it bone dry here. A few drops make no difference.
Next I have a set of drying screens (keep them clean). I put the prints down FACE UP for a while. I know the recommendation is FB face down and RC face up but I've had some problems with soft emulsion taking on the screen patter. If I leave them FACE UP for an hour or so then turn them over it seems much better.
After a day on the rack (no forced air drying in my case) they will have curled up a bit. In the winter less so but the summer can be quite humid even with my air conditioner running. At this point I use a dry mount press to flatten them. I use sheets of 2-ply matte board above and below the print. The press is on its lowest setting. Each print gets about 20 seconds in the press then out. I repeat this a few times. If the matte board seems damp I switch it for a fresh set. Always seem to have some extra pieces lying about.
So far this has worked fine. Haven't trashed a print yet (knock on wood) and I try to be very careful about washing the prints and cleaning the drying screens so I'm not worried about contaminating the matte board. Also check the matte board once in a while to make sure something hasn't gotten stuck to it. If you press it with some filth in there, it will make dent in the print.