Your 2020 candidate depends on the situation.
Obama was pushed to run despite having just entered the Senate because 2008 had no incumbents and he could establish his own image having no prior career. (This is also why Romney decided not to run for re-election as Governor.) Plus, if he lost, it was no big deal because he was young enough to come back in 2016 or even 2024 after spending time in the Senate.
2008 was a golden opportunity because W. Bush was so unpopular and the "front-runners" were both hampered by being not exactly favored by their party "when it came down to it" in Hillary Clinton or John McCain/Rudy Giuliani. During the summer of 2006, 2008 Hillary never had the juggernaut status 2016 Hillary did. Rudy and McCain polled well nationally but terribly in many of the early states.
If we assume Trump is running again in 2020, and is at least as strong as 2004 Bush minus the war fever that kept half the likely Democrats out of the field.
Working with only elected officials. A safe bet is to write off anyone who would have to sacrifice a seat in 2020 unless they're willing to give it up. Luckily for the Democrats they got slaughtered so much in 2014 they only have 11 total Senators up anyway and I don't believe any of them are states which require you to choose.
Such a term limit can encourage people to run though. It's what made John Edwards decide to run in 2004 for example.
Here's the D's list of 2020 Senators with their ages then: Cory Booker (51), Chris Coons (57), Gary Peters (62), Jeff Merkely (64), Mark Warner (66), Al Franken (69), Jack Reed (71), Tom Udall (72), Jeanne Shaheen (73), Ed Markey (74), Dick Durban (76).
Steve Bullock (54) of Montana will be the only D Governor term-limited for 2020. Jerry Brown (82), John Hickenlooper (68) and Mark Dayton (73) are all leaving office after 2018. (Dayton can run again but won't be.)
2020 Presidential front-runner and current Virginia Governor Terry McAuliffe will be term-limited out in 2018 and will be 63 in 2020.
And well, that's it. All other Democratic Governors, as of right now, will face re-election one more time before 2020. And running for re-election in 2018 and then immediately jumping into a Presidential race will be difficult. It's much easier for Senators but almost the entire Democratic field will be coming out of that group.
That leaves your best bets as someone who has no opposition in 2018 (Gillibrand), someone older who may choose to focus on the Presidency instead of another term in the Senate (Warren?), younger candidates who can take a shot at the nomination and miss even if they lose their Senate race (Casey, Baldwin, Klobuchar, etc.) and come back around again in two years, or candidates who can run for the Presidency and miss and run again for it in four years because they combine the best of all worlds (Gillibrand).
Can you have an outsider, well, duh, look at this year and even Obama.
But for anyone talking about say, Gavin Newsom 2020 let's remember he has to win the Governorship in 2018 (something he's already not a lock to do) and then immediately turn around and run for President for a year. All while being Gavin Newsom.
All of this is why the odds tend to favor the nice bland choices to challenge incumbents like Mondale, Dole, Kerry, Romney and...hmmm..Mark Warner?
Of course, Warner will have to make up the forty points he trails 2020 frontrunner Terry McAuliffe by.
He's in luck though:
Zogby Dec 2000:
Code:
Al Gore 36
Hillary Clinton 18
Bill Bradley 7
Dick Gephardt 5
Jesse Jackson 5
Bob Kerrey 3
Joe Lieberman 3
John Kerry 1
Gray Davis 1
Zogby Feb 2001:
Code:
Al Gore 44
Hillary Clinton 20
Dick Gephardt 7
Jesse Jackson 5
John Kerry 3
Joseph Biden 3
Bob Kerrey 2
Evan Bayh 2
Gray Davis 2
John Edwards 1
Time/CNN May 2001:
Code:
Al Gore 28
Hillary Clinton 14
Joe Lieberman 9
John Kerry 7
John Edwards 5
Joe Biden 3
Evan Bayh 3
Al Sharpton 2