Buying a plane & doing flying in your own plane is not a bad idea, in fact a very good one.
But it may not be the cheapest way to do your ratings. The flight instruction from a good flight instructor, parking, insurance & maintenance costs can build quickly & add up to more than it would cost you at a regular rental FBO. Also don't forget that there could be unexpected repairs from a hard landing, bird strike or anything else.
Another SMART option is do your private in an FBO or a local Flying Club & then buy your own plane. By that time, you will know if you like flying & it is for you.
Don't buy a tail wheel just because it is cheap, the availability of instructors is less & the cost of flight instruction will be more in a tailwheel. There was a thread not too long ago about the guy who was looking for a flight intructor in his tailwheel. That person took so long to get a SOLO & the cost was many times more than a private with tail wheel endt would have cost..... I think it was either APC or Pilots of America forum.....
Fly a tailwheel first & then decide if it is for you....
I know this is not something you may want to hear but this topic has been discussed quite too many times....
Learn from other people's mistakes & Evaluate all the options before you take the plunge.