Hi Max - we just traveled from Tucson to Rapid City in early October on United. It was a very good trip. The flights were on time (with one exception due to good reasons). We flew from Tucson into Denver and then an hour later from Denver to Rapid City. This was a regional airline and I have to say it worked out very well. Smaller planes, but no big deal. We did carry on luggage, but if they had been too large the airlines would take your bag right at the gate and stow it below. You just needed to wait (not long) when the flights landed to retrieve same. That was my biggest deal for us not checking bags - I don't want to start out a vacation at Target buying what I already own!!
We flew home through quite a storm and severe turbulence. We were not allowed to get up on the return flight to Denver due to same. Again, well announced and planned for by the airlines. When landing in Denver there was a plane sitting in our gate so we sat wondering how the hotels were in Denver as we only had a 1/2 hour to connect. The blocking plane finally moved, we got off first and ran. The people at the gate were great, good communication and they knew and turns out we didn't even have to run.
Overall - great prices - 3 days, 2 night hotel, 3 day car rental plus airfare for two people for just over $650. Plus, on time flights
! However, that is just airline info - I am sure many others can help you much better than I can with weather info and flying during your specific time period.