How can I calculate the maximum current a circuit needs?
Adding all the worst case currents gets you your worst case current.  Unless you need to trim the fuse as tight as possible to your actuall current, go with a little margin above this worst case.

Plain old melting-link fuses aren't for dealing with a little over current.  They are for a catastrophic condition where there is so much current that something would break, catch fire, or the like.

These kind of fuses aren't for making sure a 1 A circuit doesn draw more than 1.1 A, for example.  If that's what you're trying to do, you need a electronic fuse, possibly with a passive fuse as backup for the the really catastrophic case.  Take a look at the datasheet of a melting-link fuse.  You will see they have a wide tolerance and relatively slow response.