Every story about time travel makes up its own rules. You should decide on yours before the campaign starts. The players will come up with all sorts of head-scratchers if there aren't any ground-rules.
I'm currently running a D20 Modern campaign,
Wings of Icarus, in which the PCs acquired a TARDIS in the first episode. My original idea was a kitchen-sink, wild and wooly, anything goes, time-hopping sort of campaign. Since then it's become more focused on the PCs histories and their lack of memories regarding certain villains...but they'll still have access to the TARDIS. (And coincidentally, the campaign relies somewhat heavily on
Call of Cthulhu and
Delta Green.)
In my game, we ran up against the "genre expectations" problem. They found a TARDIS with a semi-sentient computer running it, and figured that it could do just about anything.
PC: "Computer! Analyze this future device!"
Computer: "Uh...I am a time machine. My circuits are devoted to time travel, not analysis of unknown devices."
PC: "You can
travel through time and space but you can't tell me how this gizmo works?!"
I decided to have the Hoffmann Institute "analyze" the TARDIS for several sessions, while I decided on my ground rules.
A couple resources were very helpful to me in deciding exactly what was possible and impossible regarding time travel, timelines, paradox, hard and soft loops, etc. They are:
Online TARDIS manual (especially the Laws of Time, principles of time travel, etc.)
GURPS: Time Travel
Some ideas that come to mind:
If you're going to allow the PCs to "buy" strange events that will later be fulfilled by their future selves, what is the mechanism by which they monitor events across time? How will the future selves know that a "debt" needs to be paid? Will they have fun spending years and years ensuring that a secret door opened in their past? What if they fail? Does time revert to the original event and start a new, alternate timeline (and coincidentally cause the loss of several levels)? Or is that the time for a Group Shrug? If there are no hard and fast rules against paradox, why don't the villains go back in time and kill the PCs as children? And then the PCs arrive just a few seconds earlier to stop them? And then the villains go back a generation earlier and try to kill the parents of the PCs? And the PCs follow them? If time travel/manipulation is a force in the game world, why hasn't some BBEG gone back to the dawn of time and stopped humans from ever evolving? Why hasn't a future villain come back to kill the PCs when they are 1st level? Why doesn't being saved by your future self put you into a time-loop?
I'm not trying to annoy, but you're opening a huge can of worms. It's a good, tasty, exciting, head-spinning can of worms...and fun too! But my advice is to try to know the answers to as many questions as you can before the game starts, and set some ground rules.