What do you think would be the best doctype to gain higher position in Google PR?

I would think strict would be the most benefitial, if the doctype even matters at all.

Simple answer. It will not make a difference.

Google try to reward relevance not how the page is coded. Just make sure your code is neat so the google bot can read it easily.

I haven't looked at SEO for a while now but isn't Google PR almost redundant these days?

I do not think it matters because i have been to a few websites that has unvalidated code and they are high in the search listing, so i do not think a doctype would make a big difference either.

What matters is that you have content that people want, the more they like it the higher in the listings you go hell look at myspace and big company's like that they probably do not care what doctype they use.

PageRank is created by links
it has NOTHING to do with coding "neat" or otherwise.

NOTHING to do with validation.

and absolutely NOTHING to do with what doctype you use