NGRK,
Your questions are fair, though appropriate answers would take pages and pages.
In short, definitely, owning the plane you will learn in is the very best thing to do. With the many appropriate cautions, go and buy one. It'll kep you motivated, give you excellent freedom, and keep you motivated.
I know the Thorpe T-18 very well. I believe that the S-18 is just a tricycle version of the same plane. It is a wonderful plane, (the wings are excellent), but it would not be the best airplane for a new pilot. It would make a very good second plane for you.
Tomahawks are super planes, provided that they have been well maintained, and the purchase price fairly reflects the airframe time and condition.
Arrows are great planes, though avoid the older ones. Not because they are not good, but because parts support from Piper could be a big problem. I also suggest that a retractable is adding a layer of complexity, expense, and insurance cost that you do not need for initial training.
What I have just told you is less than 1% of what you should know to be an informed purchaser, but I sure do encourage you take to plunge if it's where your heart is, just totally understand the costs to be fair to yourself and your finances.
You will probably find some good advice on the private flying forum of PPRuNe, these subjects are discussed all the time there. In particular, searches of threads about operating costs will help you, I know there have been a few. I expect that you should have more questions as you get further toward your goal....