I think classic rock, older soul / r'n'b, country, folk, blues etc. is a good start. They mostly feature simple and clear harmonies that are easy to learn by ear. When you have learned to play along to virtually any simple song within these genres by ear, you should have a gained solid understanding of basic harmony.
Latin (e.g. salsa) often feature rather simple harmonies too, but on the other hand the rhythms are be pretty challenging. Same thing could be said about a lot of the funk out there. Very good things to practice to learn to groove.
Jazz and soul are great styles for helping to build up a deeper understanding of harmony, rhythm and dynamics, but as ear training (which I see as one of the most important things every musician should learn as well as possible) it might be pretty challenging. However, there's "easy" stuff in most genres and it's great to practice a large variety of styles already from the beginning.