You can't go wrong with either airport. We recommend checking flight prices into both and making a decision from there. Denver is typically cheaper (but that's not always the case), but Colorado Springs is a smaller, closer, and more manageable airport.
The best way to avoid altitude sickness is to hydrate, hydrate, hydrate. We recommend doubling your daily water intake at least one week before the trip, and continuing to stay very well-hydrated during your stay. Don't be surprised if you're feeling a little more "buzzed" than usual after a glass of wine.
Good question! The short answer for Colorado weather at any time of the year is to be prepared for anything! The weather in Colorado can change rapidly thanks to the proximity of our beautiful mountains. March is usually when it starts to get warmer and we see temperatures in the 50s during the day, but we have also seen 75 degree hot sunny days as well as snow bomb cyclones bringing multiple inches of snow and school closings...so it's a toss up! We suggest bringing a warm jacket, even if there is no snow the early spring evenings will get cold.