When starting to become more active there's no wrong way to do so. Also, the beginning is the best time to see improvements due to the change in your routine schedule the body is prone to adapt and conform quicker. If you choose to start incorporating weights into your routine, don't be afraid to hit every muscle. The body grows simultaneously and only hitting your lower body will bring no quicker benefits than hitting everything an equal amount.
Make sure you look up the proper techniques for lifts to avoid injury and try to cater a program that suits your needs. It will take effort to find what will work best and what is optimal, but the pay off will be worth it. A great simple program to look into would be Stronglifts 5x5. This is just to give you an idea of an ideal beginner program. From there, you can explore and have a basis of what you want to achieve. This being said, below are a few links that will help show you the benefits of lifting, importance of rest (weights or not), and muscle building benefits.
Helpful Links to Check Out: