Well as a colonial I'm not familar enough with the non-star-level UK actors to hazard an opinion outside the big obvious names already mentioned here [and which I'd say there's zero chance we'll get lol]... but in general terms I'd like an actor older than Smith and Tennant but still possessing at least most of the physical energy they present. I think the kinetic nature of 10 and 11 shouldn't be abandoned...
Statham would be an interesting flashback to 9's style, but can he act anywhere near well enough for this role?
Another interesting flashback to 9's style would be Idris Elba, and I think he could contain the kinetic energy that Smith and Tennant do too. Would e the perfect mix.
A bittersweet last Doctor would be the only American who could pull off the role--
He already played a Time Lord as Willy Wonka--right down to his Wonkavator Tardis
I love Johnny Depp, but Wilder would be my choice.
In the last scene, I see the light atop the Tardis light up, and it and the roof only disappears.
The four walls of the Tardis fall away like petals. It was always just an empty box. They fade from view as they fall.
Lastly, just the square pedestal of the Tardis reamins.
On it is a single word:
That'd be quite a good way for the doctor to die. I'd want a Brit to be the last doctor though. Really I think at the end of the day doctor who is a British thing, to deliberately have an American one wouldn't really gel well with a lot of Brits. I'm not saying completely avoid an actor if he's American, I'm saying don't go for an American actor for the sake of him being American. It would also make sense for the American actor to put on a British accent too. David Tennant is Scottish, but he put on an English accent and Scotland's in Britain, so why shouldn't an American do the same?
For the final doctor, I'd like just a good standard doctor. No female doctors or any nonsense like that.
What I'd do foe the thirteenth doctors dying episode is basically do what you suggested, but a nice moment that'd make the moment even sadder would be that the doctor is on an alien planet, but he has his companion with him, so she'd (or he'd) be stranded there.
But eventually, I'd bring the doctor back for his fourteenth incarnation. Maybe before the thirteenth doctor dies I'd have the timelords resurrected, and they've brought him back to help them as there's another time war, and the 14th doctors first series would be all about preventing this new time war. The doctor would also try and bring his companion back home as he feels like he owes her. That way, they could continue with the series, and there could be up to 26 doctors now instead of just 13. Or maybe the timelords would just give him about three new lives. After all, we can't really go for 100 doctors now can we?