I would very much like to run rigid, but since it may require a custom cut and thread piece (does HD do this?), it could present problems. If I decide to use NM-U (12/3), I can place the two GFIs inside the house, bury at 12", and am good to go? It is 120V, I would have 20amp 2P breakers in the main panel. How would I come into the shed, will coming up through the floor be good enough? I might want to have conduit coming out of the ground, a service ell for looks, is that ok?
If you are planning to put gfcis before the trench at the house then you only need 12-2 wire to the shed. You'll need two runs in the trench though. You can't do a MWBC after the gfci's. That would corrupt the load side neutrals and the gfci's would trip. Also while it might be nice to only trench 12" going the extra depth is just a one time deal. No pain no gain... The benefit of going deeper is:
1) you can run one 12-3 wire in trench (instead of two 12-2's)
2) your gfci's will be at the point of use so easy to check if they trip
3) gfci's before trench might be prone to nuisance tripping
4) running mwbc to shed allows you to have (drop in nema 6-20 outlet out there) 240v in shed in case you get a compressor or welder down the road.