There are two possible ways I would suggest.
If you're sure you want to watch all of it start with the third Doctor portrayed by Jon Pertwee. Warning: These were produced a long time ago and they require more attention span than most people seem to have. They're charming if you're willing to take them for what they are.
Alternately I would recommend you start with Christopher Eccleston as the Ninth Doctor. These are paced and produced in a much more modern style so are more popular with less tolerant audiences.
My personal opinion is Dr. Who really hit it's stride under Eccleston and David Tennant and has gone down hill significantly with Matt Smith. I'm not sure if Matt could do the part justice but it's hard to tell with the mediocre shows after Russell T Davies and Julie Gardner left the show. I will always remember the days my wife and I watched this show together. I hope you enjoy it as much as I did.