From your question, it seems like you are exploring two different things: Version Control tool (VCS) and VCS Hosting site. VCS are tools like git, mercurial, Clear case etc., And, VCS hosting sites like bitbucket, github etc.,
The decision on which VCS to use really depends on your team size, size of the source code, kind of code used etc., For instance, people who code in Visual Studio use Microsoft Team Foundation Server (TFS) for version control as it can tightly meld with the code. If its a very large company or team and lots of source code to manage, then people prefer stable enterprise VCS like Clear Case. Since it's Linux systems in your case, people generally go for git or similar open source VCS [sometimes Clearcase as well].
With regards to the VCS hosting sites, Github is very popular if the VCS is git - it has desktop and mobile apps as well. It has excellent features and are used by large teams as well. Both github and bitbucket have monthly fees which are based on number of developers, number of branches etc.,
Hope this helps!
PS: If you can provide more details such as the type of code used, team structure etc., then it will help to answer the question more clearly.