You can enter a contest, a tournament or a building.
You can join a contest, a league or a social group.*
In the U.S., at least in my experience, a basketball club is a social grouping or league. Therefore you join the basketball club.
A tennis club on the other hand, could refer to the social group OR to a physical building it occupies. If you join the tennis club, you are signing up to play tennis with other people. If you enter the tennis club, you are walking in the front door. Parallels exist for yacht clubs, rowing clubs, and golf clubs.** It is impossible to not note that the pastimes for which "club" is used to refer to the building are all hobbies traditionally associated with wealth.
* If you join a contest, there is an implication of less competitive desire than if you enter a contest. You might join a charity race - mostly for fun, but you would enter the Olympics, striving to bring home gold. You could, however, join the Olympic team.
** Golf clubs, of course, can also be swung. Context matters!