Half your miles are going to be commuting. Are you planning on carrying all your stuff on your back, or would you be more comfortable mounting a rack to carry your gear? Do you have a really safe place at work to leave a $3,000 bike? Are you riding year-round in the dark and crappy weather?
You might want to leave money in your budget for a dedicated commuting bike (get a used one, cheap) depending on the answers to your question.