Github and Bitbucket is just a platform to host your code; it is relatively easier to get people to contribute to your project with GitHub if you have an open source project. Else, I would prefer to host in Bitbucket or GitLab.

About the source code control. generally, I would prefer git. You can take a look at https://www.atlassian.com/blog/git/git-vs-mercurial-why-git for making decisions.