There are 2 liveaboards and 2 land based operators in Truk. All of the wrecks are in one lagoon, max boat ride 30 mins, so liveaboards don't offer you any wrecks that cannot be reached by the landbased shops. One liveaboard anchors in a sheltered spot and divers go from there to the wrecks on small tenders just like the hotels, the other one moves around to different and you dive straight from the big boat......
For recreational diving any operator will do, and you'll have a great time because you're diving in Truk Lagoon. The dive operations on Odyssey and Truk Stop are run by expats/Americans and so they tend to give more indepth briefings and can give you more info about the wrecks (from the history to things to look out for on your dive).
For technical diving Truk Stop is the best way to go - they have the best prices for nitrox, oxygen and Helium, and have guides that can take you on extended tours (deep or shallow wrecks) and not just drop you on a wreck and leave you to find stuff on your own.
Any time of year is good - the air temp and water temp are the same all year round. Dec-Apr is the windy season where you will have a constant 25-30kph wind from the NE which causes the lagoon to be a bit choppy. From May-Nov the wind is less consistent, usually very low causing flat seas. For some reason inside the holds and engine rooms that have little circulation, the summer season tends to bring cloudy low vis while the winter time has clear water with wall to wall vis. This is only inside.....outside and spaces with good circulation are pretty clear year round.
Hope this helps, Truk should definitely be a "Must do" on anybody's list.
If you have more questions, shoot me a message.
Rob