Is traveling to home of selection in conjunction with retirement orders considered "official travel"?

It is official travel (you are considered a "servicemember in transit"). You are on movement orders until you reach your final destination. If there is any question, that's what your retirement order states.

However, I would absolutely shop around for the best price. Most hotels default to the per diem price, but that's not usually the best price you can get. For example, just doing a random look at four hotels in my area, two of them charged less for "military leisure travel" than for "official travel" (which, of course, was the Per Diem rate).