When you add a huge amount of files to git, you can't really use Git UI tools, like "Git GUI", because it has 5000 files limits for each commit. Here's the command lines that should be used to initial Git repository and add all files:
Open command line, change current directory to the folder you want to create the repository. Run the following commands:
1) Init local repository
git init
2) Add all files
git add --all
3) Commit local repository
git commit -am <commit message>
4) Create a remote repository in github.com, then link remote repository to local repository
git remote add origin https://github.com/user/repo.git
5) Push local repository to remote repository
git push -u origin master
6) Pull from remote branch
If your local repository version is behind from the version in remote repository, push command will fail. So you need run following command first then push again.
git pull <remote repository url> <branch name>
7) Ignore files
Some files you may not want to checkin to Git, you can add them to an ignore file list.