I wouldn’t use Git/GitHub to store GIS-type files for a couple of reasons
Git isn’t designed for large binary files (e.g. images), it's more optimised for text (source code or documentation). Your repos can explode in size if you store images or large binary files in there. There are various variants of Git which attempt to address this, but this is the case for standard Git.
GitHub has a 50Mb/file per file limit last time I checked, and a 1Gb repo limit (with the free account at least, maybe more with a paid plan). Same goes for BitBucket.
Having said that, Git could be useful for keeping some aspects of your projects under source-code control
- QGIS project file
- notes and documentation
- any code you write, of course :)
I just wouldn’t recommend dumping your shape files, GeoTIFFs and the like in there. Unless they’re really small and unlikely to change ;-)
Something like DropBox, Google Drive, or an Amazon S3 bucket might be a better bet, at least for data files.