My number one pointer would be to book on an airline that has a later flight to Rapid City (if one of your options does). Thus, if you are late getting to your connecting airport and miss your flight to Rapid City you should still be able to get to Rapid City on the later flight. I myself would not book anything that is less than 1 hour between flights.
O'hare has gotten better, but still has quite a few flights that are not on-time. It is my home airport, so I have never connected there. I do know many business traveler that avoid connect via O'Hare. I am not sure when their next new runway is scheduled to open, and this should help O'Hare improve it's on-time performance. At O'Hare United uses Terminal 1 and 2, so a connection on them could be a long haul. American at O'Hare is not as bad.
Minneapolis is surprisingly big, as Delta has a ton of gates that can be quite far apart.
I have not been in and out of Denver for a long time, so I can not comment on Denver.
I currently fly every week on a small regional jet, and they are fine.