I'm really surprised no-one's mentioned Christopher Eccleston.

That's who I wouId have back if I could. He was only in one series, and IMO that's not enough. He should have done another series.
Maybe have CE back as the Doctor for one more series, but have it set just after The War Doctor has changed into CE. Then end that series with CE's Doctor's Tardis arriving in London, just prior to meeting Rose for the first time. It would be so great to watch.
Ooh, I do hope that CE gives in and does this!
Also, I would very much like to see Paul McGann back as the Eighth Doctor, with some of his BF Audios turned into TV stories. The Lucie Miller ones would be great to see.

I have a crush on Sheridan Smith. I have done, ever since I first saw her In Two Pints of Lager and a Packet of Crisps, nearly 14 years ago.
Lastly, the Doctors I would like to see in a multi-Doctor story are the Eighth Doctor and Ninth Doctor. Paul and Chris would be 'fantastic' to see together on-screen.