I have a cabin in the Leadville area and spend a great deal of time there. The suggestions about acclimating to the altitude should not be overlooked. Even with the amount of time I spend at 9,300 MSL, I still "feel" the altitude, even though I am in decent shape. Hydration is key.
I have climbed Mt. Elbert several times in my life. The key for me was to not rush the climb, and allow plenty of time to make the summit, particularly if you want to avoid summer thunderstorms! It's not a technically challenging climb...just L-O-N-G!
Leadville is the place to stay if you want to do other 14er's. Mt. Massive, Mt. Democrat, and the Collegiate peaks are close by. There is also fishing and other activities in the summer. The first weekend of August, Leadville hosts an event called Boom Days. Street fair, music, beer garden, gun show, etc. Good time!