Github is a great place to store your reusable code. You can even choose to include it as a submodule in future git-based projects.
For other projects which may or may not develop into something bigger I put it on Github now that my subscription offers unlimited private repos. Previously I hosted them on Gitlab.
I like to organize the projects with Git because it'll often go months between when working on different private projects and by looking at the Git log I quickly see what was the last thing I worked on to get back on track.
No special organisation. Just git repos.
It's not great for everything but the username/projectname is pretty ubiquitous and this just brings that to your folder layouts
I include this project as a subproject in all my apps that use it.
I'n each git repository, it's a submodule.
For things I'd rather keep private I use bitbucket, who have free private repos.