Definitely do it before moving in if you can. We just had it done - we were advised about ten days and we made arrangements to move out for the first week, but we got back after six days of work to find out there was only half a day's work left. Though I did feel a few corners had been cut.
It would have been a lot easier without our stuff in - we boxed up as much as possible but the dust still gets everywhere.
Check exactly what your quote includes before deciding who to go with - we thought that rudimentary filling in would be done, leaving us with the skimming, but actually none was done at all, so we have been mortaring and plaster repairing ever since. And can't decorate until that is done! Or you could just do the easy thing and book a plasterer 
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Also have a think about what changes you want to add in - we wanted more plug sockets, some USB sockets in the bedrooms, a doorbell, outside security lights, etc. Now would be the time to think about light fittings (we added some) and also stuff like a burglar alarm if you wanted one. Outside lighting for the patio, bathroom fan, etc.
Wooden floorboards are easiest to take up. Our carpets were not re-fitted after, just put back down, but we only have two and they're not in great condition (putting it mildly) so for us it's no big deal.
Get them to check the existing wiring very carefully - the first firm we had to quote said we'd have to get the kitchen re-tiled but the second and third checked more carefully and said the existing wiring was adequate and met safety standards, which saved a lot of hassle.