The detached structure with new 2 circuit sub-panel has 2 seperate 15 amp circuits. The feeder wire will come from the main to the sub-panel 85 feet away. What type breaker is correct from the main? a single pole or a double pole? And, should it be a 15, or 30 amp feeder wire? Also is it better to use 1 240v feeder wire to supply power to the sub-panel that has 2 120v 15a circuits?
If your only power needs EVER for this is 2 x 15A 120V circuits, then you could do:
- 15A double-pole GFCI in the main panel
- 3-wire (+ ground) cable (outdoor, burial rated - not ordinary "Romex" cable) or comparable wires in conduit from breaker to the building.
You can run a single circuit of a given type to an outbuilding. You can't run two separate 15A 120V circuits. But a MultiWire Branch Circuit is only one circuit, with 2 x 120V + shared neutral. So that would work as a bare minimum, no subpanel needed.
However, a much better choice is to install a subpanel. Once you are installing a subpanel, it almost never makes sense to install a 2-space panel. If you think you'll probably never need anything extra, get something like an 8-space panel - you can get those for $35 or less at a big box store, and that gives you some growing room. If you think you will need more spaces (HVAC, tools, whatever) but just aren't ready to put everything in quite yet, consider a much larger panel. For example, in a quick search I found a 12-space panel with a 100A breaker configured to make it a main panel - you use that 100A breaker as a disconnect, so it doesn't matter if you feed it with 15A or 30A or whatever. And for not a whole lot more you can move up to a 20, 30 or even 40 space panel. Panels are cheap. Replacing a panel because you ran out of spaces is a pain.
As far as the feeder wire, whether you put in an MWBC, a small panel or a big panel, you almost always need a 4-wire feeder - a.k.a., 3-wire plus ground. If you are going to put in a direct burial cable then it pays to upsize it because replacement will be expensive. If you put in wires in conduit then put in conduit that is large enough that you can replace the wires with larger wires in the future.
The current rating (ampacity) is reference for 240V - so 2 x 15A 120V is not 30A but really 15A x 240V. But don't limit yourself.
Typical wire size (once you get beyond 15A or 20A) is 2 AWG aluminum. Basically for any ampacity beyond 20A (12 AWG copper) it generally pays to go with aluminum wires or cable.
Conduit is worth considering. In addition to allowing you to replace wires in the future without digging, conduit does not have to be buried as deep as cable, which can make a big difference.
There are multiple options. For the stated case, 2 120V 15A circuits at 85 feet, a two-pole at 240V 15A breaker feeding 4 wires (Hot, Hot, Neutral and Ground) is good, and the most efficient way. If it's a GFCI breaker it makes burying the wire to the shed easier, and provides the required protection at the shed without additional GFCI's.
14 AWG copper is fine for all 4 wires. That can be a conduit with 4 wires in it, a continuous metallic conduit with 3 wires (conduit serving as ground) or a direct-burial cable. (It could also go overhead, but that's fairly rare these days. It's an option, but not a commonly used one.)
Using the 240V feeder keeps the cost down as you get 30A of 120V circuits while only running 15A on the 240V circuit, so the wire can be smaller and less expensive.
For not much more money, you could bump this up to a 20A 240V feed with 12Ga copper. If you want to go nuts on the chance of using more power later at that location or beyond it, you could make it much bigger, but that may well be needless expense that never gets used. It does tend to be something to at least consider if it ever might be useful, when you are doing the work.
If you're quite sure you'll never need more than 2 15A circuits, the above works. If not, a sub-panel with more spaces, and larger feed wire and breaker are cheaper to buy now than when you discover later that they would be useful, and have to remove the "just big enough" things you put in now to replace them with larger ones.