I do minor weight training in the morning when I get up to keep me energized for the day.
I haven't bought my bike yet, so I'm maybe not the person to answer this, but I know all about endurance and weight training. (and when I say all, I mean a lot.) Light workouts on the middling days are good for you. It helps keep your energy level up and works out the part of you that doesn't always get attention.
If your body gets used to your workout, you will even feel odd not having it, so make sure it's something to keep you in shape and not really to push yourself, at least at first.
Pick a major and a minor upper body group to work out if you're going for strength. Do three different exercises with (I do 3) sets of 12/15 and do the exercises slowly for endurance.
your minor workout shouldn't be long, but it should definitely work those muscles!