Conratulations on your new house! We just bought ours less than 2 years ago, and only had 2 cats then. We were able to keep them at the apartment until later in the day, after we did the moving. If you can keep them out of harm's way while doing this, it's best. (I had most everything packed in advance, so they weren't upset by the apartment moving part.) It only took us most of a day to move stuff into our house; we set up the bed first (no, not what you're thinking!!!)--that way, if we were exhausted, we had a place to sleep. Anyway, we made sure all the commotion was done before bringing the cats in. We had food, water, and litter set up for them when they arrived (make sure you put the litter when you plan to keep it permanently, to avoid mishaps later!). We couldn't wait to see their reaction--the trip, though only about 12 miles, seemed to take forever! Our house was the first time they saw stairs, which was a blast to watch.
The floors shouldn't be a problem--they'll get used to it; and likely, will make a game of it, as Marge did on our laminate flooring in the foyer--the stairs are centered in the foyer, so she skidded around them, like the Road Runner--then I saw her deliberately do it for fun!
I'm sure your cats will love to explore your house--and you'll have so much fun watching them! It's amazing how fast cats take over and settle in, and become fat, lazy, and obnoxious...:-)
Best of luck in this exciting time! Wishing you all the best (and take pics!!!)