When I get a new bladder, I'll rinse it out with about a quart of fresh water with two or three drops of bleach in it, then another quart neat (the reason for the low concentration is that it's already "clean" - but you're not going to soak it, just get "warehouse crud" out of the thing. A low concentration of bleach will serve - and you won't need to spend the next hour rinsing it out.)
There are two kits you should consider getting -
Reservoir Cleaning Kit - this is a pair of soft Nylon brushes - one on a semi-rigid handle for cleaning the main bladder, and one long "tube brush" for - you guessed it - cleaning the tube. Remove the bite valve to clean out the tube. I don't typically remove the tube to clean it, but I've got the older bladders, and haven't played with the new valves yet.
Reservoir Dryer - this is a fold-up frame that you insert through the fill port. This will keep the bag open and allow it to air dry.
Before hanging the bag to dry, I'll give it about a minute through the fill port with a hair dryer on LOW or NO heat - this helps dry things out faster. Blow air in through the fill port, and let it blow out through the tube (bite valve still removed.)
I do suggest having a couple extra bite valves, and they can usually be cleaned by dunking in a quart of water with two or three drops of bleach in it and let them sit for a 15-20 minutes - then rinse thoroughly.