David Tennents run was much better, but has the issue of feeling like a direct continuation from Eccleston. He was a fantastic Doctor, but I hesitate to recommend starting with him due to this fact.
I usually point people to the 11th Doctor. Matt Smith. His run started out fresh and didn't carry a lot of baggage with it. The production values took a fairly big jump too. Most of my friends who are now Whovians followed this advice and finished the prior two Doctors after finishing Smith's run said my advice was spot on.
Once this is done then feel free to jump into latest Doctor. The 12th.
All and all this is a touchy subject for fans. I'm sure someone will chime in and say I'm crazy, but I feel strongly this is the way to go.