For an off-the-shelf kit type lean-to or gazeba patio cover, normal cost is around $10-20/SF installed - around $10-15 for simple lean-to type, $15-20 more commonly for fancier or gabled with some decorative accents or a wide variety of available colors or for ones rated for combined snow / high seismic conditions or hurricane loadings or high snowfall loads, which can sometimes push the price for a largish one like yours into the $20-30 range depending on a number of factors. In your cazse, since you are in an area with sporadic heavy wet snows and seismic issues and you want a gabled design, I would expect something around the $20/SF range of a bit more.
Specialty metal gazebo/patio/porch roof companies (not an Angies List category) and Porch and Deck contractors would be the normal Search the List category for this type of installation - also some roofing companies (especially those specializing in metal roofs) do this too.
One recommendation - actually three:
1) since you are an area with occasional heavy wet snow loads and relatively high seismic design criteria, I would be certain it is designed for your design conditions (not all kits sold meet building code for their area)
2) make sure that it does not block snow coming off your house roof. Rather than making it a continuation of the existing roof (which promotes leakage at that point and ice damming), ti is recommended to have it at least 10-12 inches lower than the roof edge, and in the case of roofs with gutters, generally coming in below the existing fascia to make it a separate roof rather than one long slope which can cause snow load and ice damming issues. Unfortunately, with a range house that is a bit less compatible, but coming off the gabled end you should be able to tuck it in under the existing gable OK - though matching roof slope may take some selecting between brands. If will be essential that runoff coming off the gable (drips and such) be handled at the pation roof at the house end - you have to properly flash it (or leave a free gap at the house) so you do not get blowing rain/snow water damaging the siding - needs to be handled like a porch roof connection if it actually goes to the house siding. Commonly, standing it off the house a foot or so works best - with the only connection being possible structural brackets to carry lateral sway loads from the patio cover, though it is usually best if even those are carried by the cover columns themselves.
3) get one with independing support columns front and back - do not "hang" it off the roof or wall, because the structural issues of doing that will make it more expensive. Tying it to the rafters to prevent sway/lateral loads does not bother me, but I have seen too many actually supported on the existing roof cause issues with leaks and roof deformation. If you really want it tied into the existing roof (more commonly done with a gabled porch roof coming off the sloping face of a roof), then instead of a patio cover you should be going with a full porch roof extension or gabled Teed-out roof - using conventional construction and properly flashed and protected valleys at the intersection of the roofs, which most commonly runs more in the $40-50/SF range. Probably overkill for what you want - normally only done for summer/sunroom additions and enclosed porches.
