i recommend using an auction house if you have a LOT of stuff that is fairly decent. they'll put it into a larger auction, keep tabs of the money that came in, give you the money less their fees (often, their fees are a percentage plus the basic cost for them to haul it away, store it, and get it ready for auction).
so, i would do three piles: trash/recycling; donations; and auctionhouse. what you are keeping, go ahead and keep in the rooms themselves, or pack up to take to the next place.
i would, personally, go room by room. when you are finished with that room, put out the trash, go and make the donation, and then separate the boxes between "moving" and "auction." you can keep them in the rooms until you are ready for the auction house to pick everything up.
call the auction house and set a date for them to come and pick everything up. this will give you a firm deadline. it will be easier to declutter quickly.
once you have all of the items packed that you want to move with you (non-essentialls), it is not a problem to store these in a place like the garage. Just make sure it is organized and not crammed with stuff. if it is crammed, then go ahead and rent a storage room.
keep the necessities at your home. remember, you still have to live there for a bit. you just want to make it easy for you to clean up if you need to do a quick clean before the people come to see the house.