I did a half marathon back in 2006 (Great North Run)
It is great fun, and its always good to have a goal...
You don't really
need to do weights unless you want to put on muscle mass... but it does no harm... I recommend you do some bodyweight exercises anyway (as you have already said)... Other than press up and sit ups you should try to do your legs and back too... you can do you legs like this:
as well as normal squats. I would buy a chin/pull up bar to train your back.
Look
here and
here for a good bodyweight training plan
Good luck and train hard