Timeless, which debuted on NBC on tonight, threaded this needle pretty well. The only arbitrary aspect of the set-up to make it all work, and keep the characters on track, was the stipulation that you can't travel back into a time in which you're alive, lest you run into yourself and cause all kinds of havoc in the time-space fabric. This is a standard ploy - I've used it in some of my own stories - and I think every story is allowed at least one arbitrary convention, as long as the rest works on the tightrope.
The first episode features our characters trying to do something about the Hindenburg disaster, presumably to stop it from exploding after its transAtlantic journey in New Jersey, in 1937. In a well-spun story that keeps you sufficiently off-kilter, something does stop the explosion - another time-traveler bent on doing far more damage to America in history by blowing up the Hindenburg on its return voyage to Germany, and with it some people to America's upcoming Second World War effort.
The good guys - actually three, an agent, a scientist, and an historian (Lucy, played by Abigail Spencer, who was so good in Rectify) - do manage to save the important people on the return voyage, but not the Hindenburg, which explodes anyway, for other reasons. A nice bow to the resilience of history to change.
There's personal loss as a result of the time travel, especially vexing to our heroes, since, again they can't travel back to a time in their own lifetimes. This rolls an excellent counterpoint to our central stories - stopping this or that major calamity, or maybe making sure it happens - the deeper personal goal of bringing back what was lost, either as a result of the time travel or for other reasons.
So we have the makings of a good series here, and I'm looking forward to more. There are some paradoxes that are not addressed or explained away by standard moves - such as the time travelers having recollections of what they changed (hey, that's a second arbitrary construct) - but it's impossible to do time travel without them, and at least they're mentioned or otherwise indicated in Timeless, rather than ignored.