chacha and waltz are slightly more approachable for beginners for reasons outlined by others (simpler steps all of the same length).

Chacha is great for much modern music, and foxtrot can be too. There is always a waltz, though it's often a faster "country waltz". But at a non dance event, foxtrot is going to be difficult where chacha is doable. (Swing also good here).

So, yeah, start with chacha/waltz. Also check out your local universities; they often have dance clubs which are inexpensive and open to non-students.