Can I safely wait before starting a mission?
This took a little hunting around to find, but here's a quick breakdown.
Guerrilla Ops, Supply Raids, Landed UFOs, Retaliation Strikes, and Council missions last for a random amount of time, between 18 and 26 hours. This time is determined when the mission is first created and presented to the player. For Guerrilla Ops, where you have 3 missions to choose from, they will all last for the same amount of time.
Other missions, including Alien Facilities and story missions, do not expire.
A "Point of Interest", which is the name for the rewards generated after completing a mission, will last between 9 and 18 days.
Missions will not expire while the Avenger is in the air, but the only effect this has is that you can't expire a mission you're flying to. If you're flying somewhere other than to a mission site, then missions can expire as soon as you land and aren't interacting with some other dialog.
Anyone interested can find the majority of the relevant code in X2StrategyElement_DefaultMissionSources.uc and XComGameState_MissionSite.uc.