Using Git with shared hosting plan
If you have no SSH access to the remote server and the hosting provider doesn't offer a git deploy feature, you won't be able to deploy directly using git.
However, it's always a good idea to track your source code regardless the remote options.
In your case, a good alternative to automate the release process would be to create a simple deploy script in your favorite programming language (Ruby, Python, Bash...) that loads the list of changed files from your git repository and performs an upload via FTP of these files.
A simple search for git-ftp reveals that there are already two projects that seems to do what I suggested:
Maybe think about a different hosting set up?
- On a VPS you have more freedom but you need to set up everything yourself.
- On a cloud PaaS you will get great technology but pay a little more.
- As mentioned above: A private repo hoster with ftp deployment option might also work.
For me, best productivity is most important. Compare costs of web hosting with costs for web development.