For your membership packages to be displayed publicly, the availability status of the package needs to be set to 'Anyone can join (public)'.
All newly created packages are set to 'Anyone can join (public)' by default.
Please note that all your existing packages will not be displayed publicly by default. You will have to change the availability of your existing packages to 'Anyone can join', for the package to be publicly available.
You can change the availability status of a package by editing the package.