Not trying to single you out mate, but as a few agreed I just wanted to point out that this is a contradiction.
To say that just a good wash and wax is all that is required and that you don't believe in paint sealants - all these are, are a modern version of the classic wax. They offer better protection from things like bird bombs and are far more durable requiring less frequent application.
As a spray painter, you should also consider that the traditional style waxes contain silicone oils. These new technology sealants do not.
Regarding paint correction and polishing a new car you need to weigh up a few things as to whether or not you should get it done. The colour of the car will be the biggest deciding factor. If it's black there might be defects that need removing. Like a car I once purchased that came with holograms (buffer trails) from the twit that pre delivered it. These should be removed. Other than that it's a matter of weighing up how much you care about the appearance versus what condition it was delivered in. I can tell you honestly my new car I purchased is white. I didn't machine this. I just decontaminated and applied Opti-Coat.
To the OP - the Pre WOW will be very effective at cleaning the trim as Dan suggested. Another thing you can try but can get quite messy is peanut butter. Not guaranteed to work but often does and most people have it in the cupboard.
For the cloth seats, we do sell a product but what you suggested will also work. The most important point here is you don't need to spend $1000 with the dealership to do this.
For the adhesive, I'd say another way of cleaning this up is isopropyl alcohol. It should remove it. Mix it 50/50 with water. Be careful though. Too much rubbing and you'll mar the paint.
Regarding what to apply to the paint, the Prima kit always works and is suitable for even those with little experience. If you are a seasoned detailer though Opti-Coat is the best choice. People do still wax it but you don't need to. I don't.