Re: How would you make "the Doctor"?
I'd probably consider the TARDIS a plot device, myself. As often as not, he can't seem to control the bloody thing, so ...
I'd probably do the Regeneration as the Healing with Resurrection adder, with a (zero-point) side effect of re-arranging his psych lims and appearance every time. The limitation of 12 regenerations would probably not be worth a limitation (since, I'm certain if the show's main actors switch out a number of times past that limit, and the how is still renewed, they'll find some way to cheat it).
Obviously, a metric ass-tonne of skills. Lots of overall levels. KS: Everything and SS: Science on huge skill rolls so he can eat the penalties for narrower subjects.