I downloaded and installed the programs offered by GitHub including Git Shell.
The problem is that I want to set up the home directory of the Git Shell program to a cust
According the article below (in the "Posh-Git and PowerShell" section) you should be able to create a Documents\WindowsPowerShell\GitHub.PowerShell_profile.ps1
file that will start when your GitHub PowerShell starts. In that file you can add the Set-Location c:\path\to\repo
command.
For what it's worth, in case anyone comes across this but has a Bash shell, adding the command cd /path/to/repo
to ~/.basrc should do the trick.
http://haacked.com/archive/2012/05/21/introducing-github-for-windows.aspx