As I'm looking to my future health, running long distance doesn't seem to be in the cards for now. I mentioned before I would like to start some basic strength training. I don't want to bulk up - just would like to do some different types of workouts that I can do at home. I still will run - my thoughts right now are to run at most 3-4 days a week. Basically 3-4 mile runs during the week with something in the neighborhood of a 7-9 miler on the weekends.
During all this, I would like to add the strength aspect. Just not sure how to go about it. Or how often I need to do it to get any kind of results. I guess I just want to strengthen my core, and just get stronger overall. I don't want to feel I have to work out every day - my body and overall soreness just won't be able to tolerate it. But is there a mix that makes sense? Is there a number of days I will have to do strength training to get the benefits?
I have a free weight set at home, so I know I can do reps with low weights, which is all I am capable of. So I'm thinking some weights for upper body, planks and sit-ups for my core, and some squats and such for the legs.
Where do I start?

Do you guys have any plans you follow? In my head I'm thinking this right now:
Monday: Strength training (30 minute session?)
Tuesday: 3-4 mile run
Wednesday: Strength training (30 minute session?)
Thursday: 3-4 mile run
Friday: Rest
Saturday: 7-9 mile run
Sunday: Strength training (30 minute session?)
I need some help please.