beginning weight lifting? HASfit success?

Queenofthezoo

I am very much a beginner when it comes to any type of fitness and exercise. I have found that I enjoy the Leslie Sansone walking youtube videos (thanks to those that suggested that), but keep seeing on here that I should lift. I bought some basic weights (3,5, and 8 lb). I found HASfit beginning weight lifting for 15 minutes. It is very basic, but I can actually do it and not feel like a total loser that can't finish a basic work out.
Going to a gym isn't an option. And I think I would need a personal trainer at a gym to even begin to consider lifting barbell/heavy weights/etc (honestly I don't even know proper terms or names of things, or anything about it).
But are these small weights and a simple 15 minute hasfit routine done daily enough to make a difference? I really am trying to do this "right", but I just don't know what I am doing. I am afraid I will hurt myself if I try anything more than the very basic, but then I wonder if the very basic is going to make any kind of difference. I just want to be effective with whatever I do. So where do you recommend a 32 yr old overweight never-been-athletic mom focus her energy.
I don't just want to be thinner, I don't even care about being super "skinny" I just want to be comfortable with my body, and healthy and STRONG.