CDX or OSB is exterior sheathing normally used. Match the thickness that was used originally (probably 1/2"), then minimum of 15# felt then the roof shingles.

1/8 in gap between sheets.

Yes, good point brick and thanks for picking me up!

Many thanks for your advice!

The thickness of the sheathing depends on the spacing of the rafters and you didn't tell us that so I would recommend at least 5/8" CDX plywood or Oriented Strand Board.

Asphalt saturated felt (building paper) underlayment once weighed 15 lb per 100 s.f. but it is now much lighter and therefore called No. 15. To match the original standard it is necessary to use No. 30 building paper.

The shingles may have lasted 25 years but obviously they did not protect the sheathing so the design was inadequate possibly because of a low slope. If you want the roofing and sheathing to last another 25 years install an underlayment of self-adhering Ice & Water Shield from Grace without substitution.

A little overkill in my mind for a shed, Reno.

Making a building last more than 25 years is not overkill to me.

"Making a building last more than 25 years is not overkill to me."

Depends on how large it s.

Not everything needs to have a long life.