Your questions are very generic and beyond the scope of support that we can offer in this forum.
Please have a good look at the Requesting Help guidelines. It offers some links to general web development and learning the basics of Git.
With the above said I will offer a couple of pointers.
Since you have a lot of images you need to either look into hosting them on a third party service and call them in your content files. These images should not be hosted in Git because as you mentioned the repo size will grow and sooner or later you will end up having problems.
Another option would be to generate the site locally and then simply upload it to a service like Netlify that supports deploying a website from a folder without Git. Also Netlify has a more generous free storage plan. Look it up on: https://netlify.com
If you decide to use Git you will need to upload the entire folder of your Hugo project to its remote repository.