I would not put the timer in the LINE side of the GFCI receptacle. It might, as you suspect, cause it to trip when the timer turns on, just like some of them trip when you restore power at the panel or after a power outage.
I like the idea of using a 3-wire timer instead of that electronic (Triac controlled) one.
Install your GFCI receptacle in the garage (or other indoor location), connect the timer to the LOAD side of the GFCI, and then run your UF cable (needs to be UF if you're exposing it to the weather, but not if you're running it inside, to a box mounted outside, as long as none of the cable is exposed to weather) to the outside receptacle, which would not need to be a GFCI, since it is protected by the one in the garage.
The timer should be the permanent mount type (wall switch, or stand-alone box), so it can be wired directly.
I still like the old mechanical ones that have a heavy switch. They're enclosed in a metal (or plastic) box with KO's for your cable.
Nice thing about mechanical, is that they won't go wacky on you if the power dips, or you get a surge.
This is the one I am talking about