What can I build/use for a door in an old barn?
One simple and classic option would be a sliding barn door:



You can make the door whatever size you want. You attach a rail to the outside of your shed, some rollers to the top of the door, a handle, and perhaps some retaining or locking hardware. You can make the door in a traditional rails/stiles approach or just cut a piece of plywood to size and paint it.

Here's one idea for a cool look with moderate effort. I haven't done this but am considering it for some new shed doors.


Get a piece of plywood and cut it to size.
Attach 1x6 wood along its outer edge so it looks like it has stiles.
Cut some lights. You can do simple rectangular ones or get fancy with a jigsaw and cut in some fun designs, your initials, whatever. Because you're working with a piece of plywood you have a lot of options.
Prime &amp; paint with good exterior paint.
Attach some acrylic/plexiglass behind your lights (glue, caulk, and/or window glazing compound depending on your design, plus a few screws around the edges).