1. Why are you looking at light sport? Is it a medical issue? If not, then I would just get a full blown private ticket and if you want, you can let the medical expire and exercise light sport privileges. Talking to people around here, the real world times between the light sport and private ratings are not that different and private has some advantages (plane, altitude, speed..etc).
2. A better quality plane is more important than the type of plane. For example, I'd rather have a very good condition "B" than a marginal "A". So while the "A" may be the better type of plane, the better condition of the 'lesser' plane would make it the better buy. So a prebuy is imperative and DON'T get in a hurry. (more on this later).
3. Don't discount some other type of planes. My first plane was a Quad City Challenger II Clipped wing special. It was a great plane and if it was not for the two stroke engine and the desire to fly acro, I would of kept it. I bought it for less than 10K, had the engine rebuilt for 1400, bought a new prop and some other stuff and still broke even when I sold it a year later and 113 hours later.
OK, the two stroke.... I only had the plane 113 hours. I had one engine issue that was my fault and one that I never figured out what the heck happened. None of them resulted in an engine out for me, but in the year I owned my two stroke I personally knew three guys that flew with me - Two had engine outs, one had two engine outs. It may be easy to say these guys just don't know two strokes, but one has been flying two strokes for 20 years and was on the EAA's Ultralight Council and the other has been flying two strokes about as long. Compare that to people I know that fly 4 strokes and I have known lots of people over 20 years and three of them have had engine issues and none of them caused a crash (blown jugs). If you have a very good grasp of 2 strokes AND a good support base, they can be fine and I LOVED the way the Challenger flew. In the end, I never trusted the two stroke and since I wanted to do acro, I sold the plane and bought a 7ECA.
Now about not rushing.... The desire to buy something is strong. BUT, you don't have to buy to start learning to fly. I'd start learning to fly now and this will help take some of the pressure off wanting to buy RIGHT NOW. This has an added benefit of not only removing the rush to scratch the 'itch', but will also give you experience. This experience gained will give you a better idea of what you want.
The benefit to renting when you start is it lets you fly several different types of planes. Maybe you will like to open cockpit feeling, maybe you will hate it.... You don't know which it will be until you try it. Maybe you want a taildragger, maybe you hate them... You don't know till you try them both. The type of plane you buy is all on what you want to do with it. I like acro, so a non-acro plane is not an option. My buddy just likes to put around, so his favorite plane is his J3. Another buddy thinks that a plane is worthless unless you can fly it 1000 miles IFR so he wants a Bonanza over any of the preceding planes.
I'd suggest you start taking flight lessons now and try to fly different types of planes.
A few other points..... Hand propping. I don't mind it when I have a buddy, I don't like it by myself. Opinions will vary. As others have pointed out... Buying a plane is not a forever deal. I have been an aircraft owner for a little over three years and have owned three planes (maybe I should of taken my own advice???).