I like the Sport Pilot rule, but think they should have gone farther and restructured the entire Pilot certification process. Make it more of a stepping stone.
Take lessons, get signed off for solo, you can now fly your plane solo within [5/10/20/??] miles of your airport forever. You now have a Solo learners permit. You have to have a flight review every year, or whenever you haven't flown in the last 90 days to maintain your limited priveleges. Can fly C172 class aircraft or smaller P/W ratio. WX mins 5000/5, Daylight.
Continue your lessons, cross countries, night flights, etc and earn Solo Pilots License. You are still limited to the C172 class P/W but can fly solo anywhere in the country that any other pilot can fly. WX mins 5000/5
Continue training, show more knowledge, etc. get certified as a Sport Pilot. Now you can carry a passenger in that C172.
The next step would be what is now the private. The only change would be that it is now a "Recreational Pilot", since it can not really be used efficiently for much more than recreational purposes.
What is now the instrument ticket would be the "Private" license.
I don't think there needs to be any minimum hour requirements to start any of these phases. It is up to the instructor to determine if, and when each pilot is ready to handle the tasks associated with each particular level.
I also don't think the medical should be required, if at all, until the Private/Instrument level.
As for the type of aircraft, I think the C172 and similar aircraft should be included in what is now the LSA category.