At the very least a drill and a circular saw unless the shed is kit form, I don't think any power tools at all would be needed.

For anyone using power tools having the correct safety equipment and being aware of safety procedures when using power tools is important. Power tools are very dangerous if you are not aware of the safety measures involved when using them. You need to be focused when using power tools, as unlike hand tools power tools can keep going when you don't want them to. Here are some essential factors beginners and general users need to take into account.
Power Tools Shop

You're in the "electrical" forum, and while power tools
are certainly electrical, I think the forum generally
answers issues having to do with electrical circuits
and repair. Maybe one of the "exterior" forums is
the place for you.

That said, the basic power tools are 7in. circular saw, jigsaw
& VAriable speed Reversible (VAR) drill. A 10in. table
saw is next, esp. if you're going to be rip cutting the
lumber. A 10in. mitre saw for joinery and trim. If
you're going to be doing finish work, a 1/4 sheet sander. If you're going to have to do any kind of
work on existing structures or demolition, a
reciprocating saw (saws-all). For interior carpentry, a router (probably not useful for a
shed). After that, things get big, stationary and
expensive (drill press, etc).
Stuart