I have, after two years, finally talked myself into putting Relic into the washing machine instead of bathing him by hand in the bathtub.
I was very much still concerned that the machine would literally chew him up, but after the cycle was done I went over all the seams closely and found that he had weathered the washing with no issues.
After turning him back right side out I placed him on the rack to dry as usual. I do not recommend hanging a fursuit on a hanger to dry. The weight of the water that still needs to be taken care of can really be murder on the seams, especially those that are hand sewn. On top of that fur has a tendency to stretch a certain amount as well, you could find your suit a touch longer than was, so honestly if you have a rack of some sort (we have a large heavy wire frame dog kennel that works great) use it to lay it out flat to dry.
I have heard others say that you should brush several times as the suit dries, I wait until it is dry and tend to the brushing then and have never seen any difference between doing it either way.
Once dry and brushed out he's ready for a spray of suit deodorant and to get rolled up and put into the case for storage until the next event.
As for a rack to dry it on, if you are not as lucky as I to have the large kennel, I also have made myself a drying rack that I can place over my bathtub for the purpose of drying. Available at any Lowes or HomeDepot you can get two sections of wire shelving and have them cut to length to fit over the length of your tub. 