It's the latter; we have a menu of missions that you select from in the safehouse. Mike warps to mission, beats up/stealthily passes by a bunch of bad guys, and then you return to the safehouse to check your news, emails, etc., and repeat the process.
How much will in mission decisions affect other missions? Will there be stuff like, for example, having a new entry point for a level because you finagled some explosives during a previous mission, or finding helpful info on a mission building's security system, while accomplishing some other task?