To Begin with First or Third Doctor?

I just picked up a BritBox sub (in USA here) and wanted to go through the classic Who archive for never saw much of it.

Logically I'd want to start at the VERY beginning, but the missing links, especially on Second Doctor's tenure, makes me uneasy going that far back for I'd lose some story. In particular, BritBox doesn't have The Tenth Planet, where First becomes Second.

The other logical entry point is starting with Third Doctor (whom I already have some exposure to and like) - for one, color, and for two, BBC stopped misplacing episodes.

Just looking for some honest feedback. I've seen all of Modern Who and wanted to check out the old skool stuff.

(By the way, I have no plans on 'skipping around'. I'd just watch from the start, taking my time to savor it. Saw that Tubi might have some that BritBox doesn't of the missing 1st/2nd serials. Still want a good source of Tenth Planet.)