I wouldn't leave out the claying on a new car. Many times they have surface contamination from the way they are transported. Rail dust is a big factor with many new cars.
Also, you must factor in the dealer "prep". Unless you tell a dealer not to touch the car, chances are they will install swirls and micromarring from their bad washing, polishing and possibly waxing technique and the tools they use to do these tasks are usually cheap garbage making the dilemma even worse. Best bet is to insist that they not even wash the car and you learn what to do by reading and studying here and downloading the free e-book.
Otherwise, your routine looks fine but you may want to use a mild polish before AIO depending on what the car looks like. You can apply all by hand with a foam applicator as mentioned or if you have a PC, you can apply any polish or the AIO that way. I like microfiber applicators as well. Get yourself some good quality MF towels too, they are amazing.
Good luck and have fun!
Eric