Hydro is pretty unique stuff. There are a few things out there that SAY they are "wax as you dry", and I used one when I was out of town and had no Hydro on hand, and it was a disaster.
As far as wax...you probably should wax it when you get a chance. Generally the stuff the dealers detail with is not great quality or lasting power. The first thing I did when I got my car was strip it down and start over.
The Simoniz wash...I can't speak to. Wash is generally wash but if it's something "over the counter", I tend to stay away unless it's Meguiar's. But there are a lot of people that use a zillion kinds of wash; as long as it has decent lubricity and glides over the paint it should be fine. Drying without spots...I'll believe it when I see it

That generally has very little to do with wash soap and more to do with highly filtered water. You'll have to let us know how it goes.
I would recommend though, if you're going to get into really keeping it spotless and looking great, you check out some of the premium brands if you can afford them. Lots of people around here like Prima, Zaino, P21s, Meguiar's...I'm sure there are more.
As far as inexpensive and not having to order online, I'd go with Meguiar's stuff if someone took away my internet and made me shop at AutoZone

Except that IMO the wax is nowhere as good as Epic (and the spray-on wax is EVIL!

). The rest of their stuff works fine.