For backpacking, I too prefer a long sleeve shirt. I hate wearing sun screen for extend lengths of time (greasy, picks up dirt, blocks pores). So I got with the shirt (and dorky sun hat combo). Affords bug protection, sun protection and easily buttoned up or down for ventilation.
My go-to place for such shirts are the thrift stores. In Helena, MT on my CDT hike, I picked one up for the princely sum of $4 after a deer ate the buttons off my other shirt in Glacier!!! Both were old polyester dress shirts. I've even worn the 65/35 blends over the years and did OK. :) The shirts have lasted many miles each. I only got rid them because my much more sensible female companions over the years made the point that the shirts were a bit, er, worn in... ;)
I am quite the fashion plate on the long trails, aren't I? :D