One trench the whole way will be easier to pull cable through. You could make it direct, one straight line, or closer to it than otherwise.
Fences can get blown over, run into, replaced for service, or removed for aesthetic reasons, which will become more of a pain to deal with if you run conduit along the fence. Also its less pleasurable to look at conduit than to not.
Your municipality or county should be able to tell you your local minimum depth for buried cable. It depends on your jurisdiction if you're asking about code as I assume.
I would recommend oversizing the conduit significantly to make pulling easier and allow for easy upgrades in the future. 2" can't be that much more than 1". It will be more durable and it could save a lot of work later on.
You can save costs on grounding by using bare wire, or using metal conduit as your grounding conductor. But I would not bury metal conduit to avoid dealing with corrosion. Even a bare ground conductor inside a plastic conduit is going to fare worse than a sheathed over time.
Paint a white line where you plan to excavate and call your utility locating service out to mark obstacles. The white line or shape will keep them from needing to mark unnecessary things in far off parts of your yard.
Rent a trencher and make the work easy on yourself.
Bury conduit larger than you need, because excavation sucks.
Dig depth is often 2foot minimum for nonmetallic, 6 inch minimum for metallic, but ask your codes department what they will approve.
For wire gaguge, use a calculator like http://wiresizecalculator.net/.
By my estimate you would want 6awg, but maybe the direct patch can cut down distance and let you use smaller.
I've said it before, and I'll say it again. It's tough to beat a 60 ampere sub-panel. You might be able to get by with a 40 amp setup, but it's always nice to have future expansion possibilities.
At 90 ft., you're probably okay to use 6 AWG copper, or 4 AWG aluminum conductors. You'll have to pull four conductors, either through conduit or via a cable.
Since it's a separate structure, you'll need a grounding electrode system. Which you'll have to bond the grounding conductor from the feeder, and the grounding conductors within the building to. You'll keep the neutral conductors isolated from the grounding conductors, which will likely mean removing a bonding jumper within the panel.
Best Answer
Just drop a conduit in there instead, you'll thank yourself later
Instead of rushing to buy wire and getting the wrong thing, then having to dig it up later, why don't you get yourself some fat PVC conduit (such as 1.5" or 2") and lay that in the trench instead, with prefabricated sweeps and expansion fittings at each end? That way, you can pull the wire at your leisure, and don't have to worry about digging things back up if you want to upgrade later. While you're at it, you can also lay a second conduit, say 1", if you want to to provide a convenient way to run a telecom cable (of any sort: phone, Ethernet, fiber, you name it) out to the shed.