When are you going to hire this contractor? 2 years when you replace the siding? Depends, of course, on your budget. When the company I work for builds/renos a house, and it is new roof/siding/windows, the roof is the first done. Then windows, then siding, then gutters.
As another poster said, the gutters are only attached to the fascia, which is independent of the roof itself. The fascia is usually replaced as part of the trim of the siding, along with the soffit. Gutters are pretty much the last part of the project.
In terms of cost, it will probably be cheaper to do everything at once, but that is a lot to bite off at once. hope that made sense