I was where you were a few years back. Wife (then girlfriend) and I were both gainfully employed pre-Navy, but not married. We left a lot of stuff at parent's places and grabbed it once I got to a fleet squadron and knew I wasn't moving for a few years. I'd plan on living lean during flight school due to the multiple moves. Movers don't give a shit about your stuff, and they're a necessary evil of this game. Plan on at least 3 moves in flight school unless you're really lucky.
I'm fairly certain you can get DITY weight for the motorcycles if you trailer or UHaul them, for whatever that's worth. Partial DITY is probably your best bet, leaving some stuff behind in storage. You DITY the essentials and the bikes, maybe come out a few bucks ahead, movers take the rest.
Also, keep in mind you'll probably be at OCS, with minimal connectivity, while your wife is trying to do this full DITY move, by herself. Maybe she's down for that kind of thing, but you'll have been out of pocket for 12 weeks and making her move by herself? Not a great plan. I don't know what kind of "moving leave" married ENS are getting in PCola, but I don't remember it being very much back in 2010. So if you push it to your "moving leave" or whatever, it's still going to be a hot mess trying to box up, truck, and drive it down in whatever minimal time they give you. Oh, and you'll be trying to actually find rental housing at the same time.