A pure STR paladin build is going to be problematic. A CHA/STR paladin, particularly of the Dragonborn variety (CHA 18/STR 16 at 1st level), works fine.Paladins are hands-down the worst designed class in the first PH; setting aside how weak their mark is, there are significant gaps in the choices available to both builds, but the strength build in particular
The paladin mark isn't very effective, but, practically speaking, I haven't found it to make much of a difference during play.