If you have the means, and are at the starting point of zero hours, purchasing your own plane to use for your training will be an advantage- IF you purchase a solid plane. Bear in mind anything you're looking at buying is likely 40 years old, and the examples you'll come across will range from pristine hangar queen to something that should be sold for parts. Prices will vary accordingly. When it comes to buying old airplanes, buy the best plane you can afford, as it will likely be the cheapest to own for your duration. If you go down the road of buying a plane, make sure to get a pre-buy done by a competent mechanic.
For something like a PA28-140 or a C-150 I'd estimate direct operating costs around $30-$40/hr, with fixed costs (hangar/tie down, insurance, the aircraft loan payment, etc) variable depending upon the amount financed, how insurable you are, and the geographic nature of where you would be keeping and flying it. Also bear in mind, that you are very wise to factor in a mx reserve to handle both planned and unplanned service.
Assuming you buy the right plane, you can likely fly it several hundred hours over a year and then sell it for close to what you paid for it. Now, factor in the cost of instruction and checkrides, and there is the cost of attaining your ratings. Of course, there are still plenty of real life variables that could fudge those number up or down, as you have now added risk to the equation when you own your own plane.