The roof has a shallow pitch (4 in 12?) and a single layer of asphalt shingles in bad condition. They are not curling much but they are badly weathered and missing many edges. And there are plenty of leaks. I don't know how long the roof has been leaking; it leaked already when we bought the house last year. (We factored the cost of a new roof into the purchase price.)
Part of the roof is over an attic. Under the shingles is tar paper over sheathing. From inside the attic (crawl space) in many spots the sheathing is cracked or broken. The roof has an 18" overhang and neither soffits nor ridge are vented. The attic has gable ends with vents but at one end the vent is covered with siding.
Another part of the roof is over an addition with a ceiling of exposed rafters and tongue&groove boards. I don't know what lies between the asphalt shingles and the ceiling. Probably not much, because the addition gets very cold in winter and hot in summer.
The house is in very sunny and dry New Mexico at 7000' elevation (so nights are cold). It has no AC nor a swamp cooler but is cool in summer thanks to deciduous trees that overhang the west side of the house (blocking afternoon sun) and good cross ventilation. The climate is "high desert", so heavy snows, monsoon rains, and significant hail storms are normal.
A recommended local roofer proposes to strip the old shingles then install new shingles. I anticipate once the old shingles are off I will hear that the sheathing needs repairs and the roof needs to be vented. Should I go with stripping the old shingles? Should I plan to replace the sheathing?