General Rule of Thumb - Always take the first available flight at the start of the day ! Do not wait till later in the day when all the normal snafu delays cancellations oversales reroutes skewer the space available picture. Even more important if you are in a bottom of the barrel class of pass or ZED fare - think of all the previous situations where higher ranking pass riders have the same problems thrust upon themselves and then they get merged into the pool making non-rev space available travel even more troublesome. So you get to the connection airport and have to wait a few more hours at least you got to that point and other options maybe available. Note that you are traveling DEN-MSP; that is a non-stop flight. Where are you connecting from at DEN or continuing on to at MSP ? That is important because connections at DEN could maybe made better at SLC a large DL hub or instead of making a connection at MSP maybe DTW (Detroit) or ATL (Atlanta) maybe a better option. Delta's system is so large that a multitude of options are available - tells us more - but plan on a early "First" AM departure if possible to get the best potential to arrive at your destination. Last Rule of Thumb "Avoid the last and ONLY flight of the day UNLESS it is all that is left for consideration and you are stuck with it" !