What are the best things to do when joining a new club?

As excited and enthusiastic and correct in your assessment, don’t suggest improvements to the infrastructure early on. Even if they would absolutely greatly benefit the organization (I say that quite honestly) if your suggestions are resented, they won’t be heard and you’ll never be heard after that.
Also, chat up the members. Even if you abhor small talk, do it anyway, it’s a good way to start understanding who is who, and with whom you might have the most in common. Do as many activities in the beginning as you can schedule, until you find out which ones interest you the most.
Have fun. (If it’s that kind of thing) Be involved.
Can you say what kind of a club this is? I’ve been the new kid a few times (moved around a bit) so I’ve learned a few things.

Right @JilltheTooth

Just be friendly, show enthusiasm for being involved and don’t take on any sort of a leadership attitude until you have ingratiated yourself to the group and then you can certainly make suggestions. You’ll get a feel for the different members and the overall energy of the group soon enough. Have fun!