What diameter PVC conduit should I bury under my front yard?
Code defines minimum sizes, based on fill percentage. Larger also meets code (by exceeding it.)

Anyone who has ever pulled a conduit at/near maximum fill % (40 for 3 or more wires in conduit longer than 24") can tell you it's not fun to do.

You have a short run across the yard, so the conduit expense is not a huge factor. In general, the conduit expense is always much, much less than the trench to put it in expense.

I would use schedule 80 PVC for a job like this; while it will mean finding your local electrical supply unless you have the oddest home cheapo I've never met (never seen sch. 80 at any of the ones near me, other than the odd sweep) it is far more robust than schedule 40. I would also use 1 inch - not because "code says you need it" (it does not) but because it is somewhat stronger and provides considerably more room than you require - and more room makes pulling wires easier. It also means you don't really have to define exactly what you are doing (so the absolute minimum size you need can be specified) because it's more than large enough for considerably more than you have stated no matter how you do what you've stated. 

I would (but you don't need to) put in a second 1" conduit while the trench was there, if there was the remotest chance on the face of the planet that I might ever want to run phone, network (perhaps an outside wireless access point), garage door opener or any other sort of low voltage wiring to the location. See cost of conduit .vs. cost of trench again. But it's your call.

Finally, don't skip the "buried electric line below" warning tape in the top 6 inches of fill for the trench. Digsafe won't know your private line is there, so they won't mark it.