Service clubs like Rotary and Kiwanis are primarily business people; in fact, there has to be an 'opening' within the local community club for a certain 'profession' or 'service' in order to join, since "doubling up" of professions is discouraged to avoid competitiveness (and you need a sponsor already within the club). Although they do community projects, the idea is to seek out the services of a fellow Rotarian, if possible. Many small communities will have multiple chapters that meet (new branches open in a neighboring area), since the older ones tend to be full.
Chamber of Commerce is all about small businesses, and it's a good way to network within the community to get to know the other small business owners, esp if you your community is small enough to rely on 'business-to-business' sales (rather than everyone going to the big chains (like Costco) for their business needs). They have an ambassadors program, where they'll conduct opening events for the newest members (businesses pay to be members) and their mixers are an opportunity to shmooze with the other members.
So none of those are particularly 'social clubs' per se, where the point is to make friends; for that, you might be better off finding groups that do volunteer community clean-ups ('clean a beach' activities) or even a nature club that has day hikes, etc. Many junior colleges offer night courses for adults who aren't necessarily seeking college degrees, but simply to learn additional skills to expand. Those are always good; in fact, look into the local junior college and sign up for a night course that seems interesting to you, and learn simply for the sake of learning, or to explore a new topic.
It's always hard to get out of your rut and go into something new alone, but go in with a good attitude and wearing a smile, and adopt receptive body language, and be open to meeting people.
Adam