If you’re using any sort of legacy version control, whether commercial or open source, you should switch to git. If you’re not using version control, you should definitely switch to git.
Choosing a platform
Several vendors offer “git as a service”. Github is best known, but Atlassian Bitbucket, GitLab, and others are popular.
Cloud services versus in-house
Many companies are uncomfortable with the idea of putting their source code on a cloud-based service.
If you don’t have a real business requirement (that is, a regulatory requirement) for in-house, then I would strongly encourage you to use a hosted service. They are state of the art products in a highly competitive market, by far the best version control tools ever offered. They all go far beyond git itself, providing a wide range of advanced services like problem tickets, continuous integration, and blog hosting.
But if you absolutely must use an in-house solution…