A relatively inexpensive option for the basement and convenience would be an adjustable dumbbell set like this or this. You have the option of starting as light as you need to.
It is easy to overlook the legs, the largest muscles in the body, when you use dumbbells because they seemed like you’d only use them with the arms, but this is not true. Some of the exercises with a dumbbell are quite similar to a kettlebell.
I am posting two well-done videos for full-body dumbbell workouts. The thing with resistance training is that you have to remove the barrier to your actually doing it, and for many folks this means being able to do it at home. It would be great if you joined a fitness center and worked with a personal trainer and so on, but if that does not happen, do this or one of the other options presented.
12 Minutes
A well-done instructional video in a British accent. Remember to start with light weights the first few times until you get your sea legs.
40 Minutes
Another well-done video with good instruction is presented here.