If you just want to train your push/pull skills you can definitely create a GitHub project and then use that.
The way to do it is to go to your GH account, go to new repository
, then when you create it you'll have this screen infront of you.

You can see that there is a section for ...or push an existing repository from the command line
. Execute the two commands you see there in your local repository and then you'll be ready to go!
But wait, there is more. You don't even have to use GitHub to have a remote! You can have your very own remote locally!
You can create a local directory, let's call it local-git-repo.git
mkdir local-git-repo.git
Then in it we can execute
git init --bare
Then in your actual projcet you can do the following
git add remote origin <path to your git repo>
and done! You have your own local repo which you can maintain!