I would prefer to use blog.mydomain.com and then do a 301 redirect to bring all Google juice into the main domain.
As far as the guessing for blog name if your 404 pages are good enough it won't matter, for me if you go to http://whyspam.me/blog they'll still see the link to the blog, even though you're viewing a 404 page.
301's do dampen PageRank as well, though the exact amount is not known. I've always put it around 10-15% (i.e., after each 301 you are left with 85% of the original value). I also suspect that its contextual - so a 301 from www.mydomain.com to mydomain.com would probably be dampened less than a 301 to a completely different domain (e.g., bit.ly).