Sounds like your doing great. The key when you up your distance is to do it slowly. build no more than 10% a week on your distance. Make sure you do plenty of stretching particularly AFTER you run. For core work I just do various situps and pushups. At 42 your not that old to start. I'm 52 and started at 47. The key to keeping it going is getting into a dedicated routine.
There is a lot of useful Web info on weight training and core strengthening exercises, but I would also recommend investing in a session with a personal trainer who can provide you with a customized program tailored for runners. I did that about a year ago and found it very helpful. I did one session with a trainer affiliated with my gym and received an excellent set of exercises tailored both to complement running and to my body's individual strengths and weaknesses.
Heart of the City Run, Los Angeles, CA, 24:13
Downtown Anaheim 5K, Anaheim, CA, 24:32
Claremont Turkey Trot, Claremont, CA, 24:20
The Great Race - Old Agoura 10K, Agoura Hills, CA, 51:12
Fiesta Days Run, La Canada, CA, 49:31
LA Cancer Challenge, West Los Angeles, CA, 51:21
Long Beach International City Bank Half Marathon, Long Beach, CA, 1:54:31