This is totally frivolous, but this seems like the sort of thing you'd have some thoughts on — how would one rank the Doctors in term of fame/notability when they were cast in the role? Going from 1 for most famous to 11 for most unknown, here's my initial stab at it:
1. Peter Davison (I'm giving him the nod as All Creatures was a popular hit in the UK when he was cast, whereas Eccleston's films typically more prestige fare and his big TV roles were about a decade previous...)
2. Christopher Eccleston (...although I'm willing to be convinced otherwise)
3. Jon Pertwee (Light entertainment and radio work probably makes him the other "name" actor to be cast in the role)
4. Paul McGann (Alien 3 might be the biggest movie a Doctor made before being cast, but I suspect he was more a familiar face than a really known name in 1996)
5.David Tennant
6. Patrick Troughton (I'd say Troughton and Tennant are toss-ups, in that they were both working actors with some moderately recognizable performances but who clearly hadn't broken through pre-Who. I'll give the edge to Tennant, just because he had Blackpool and Casanova shortly before Who, and I don't see the equivalent on Troughton's CV in the 1963-66 range.)
7. William Hartnell (People were probably vaguely aware of him, but "stardom" seems a particularly nebulous term when applied to 1963 — William Russell was the bigger name in the initial cast, right?)
8. Tom Baker (He was Rasputin in Nicholas and Alexandra, but that really seems to be the only role of particular note pre-1974)
9. Colin Baker (A working TV actor like Troughton, though I don't really see any notable pre-Who roles on his CV)
10. Sylvester McCoy (I'll roll with your judgment here — it seems like he was well-known in comedy circles, but I suspect that meant he was unknown in all other circles in 1987 Britain)
11. Matt Smith (Unless Party Animals was a bigger deal than I think it was — certainly possible! — then it seems like he's the closest the show has ever come to casting an unknown)