I love Three's era! In some ways it's like Nu Who, in that the close ties to UNIT especially in the early seasons give it a bit of coherence. There's some killer episodes in there, and some excellent companions. Even Jo grew on me, though it took a while for me to warm up to her after the magnificence that was Liz Shaw. Although... don't you like Liz Shaw already? How much of Three have you seen?

In your position I'd probably watch straight one-two-three. Hell, maybe I'll do a watch/rewatch myself. My reasoning is: there's not actually that much of One and Two to watch, with their comparatively shorter runs and their missing serials. So watch them, bemoan the missing episodes, and then finish strong.