He was supposed to play himself but I think it's safe to say that Pertwee was a very humourous man. They joked so much on the set (apparently, Nicholas Courtney and Roger Delgado were also quite funny) that the producer told Pertwee once that he wished he'd take his work more seriously. (see "Return to Devil's End" for more)
Considering the dialogues full of witty and joking remarks, the costume deliberately chosen because it looked the most absurd and the weird car, I can't really comprehend people saying that Pertwee's Doctor was played in a serious and straight fashion, or even calling him the most serious and straight Doctor. Surely, Eccleston was a lot more serious as a character? But whatever, this is a subjective question and people will come to different conclusions. However, I would urge you to rewatch the show sometime.