Yes, you should use GitHub for your public and private repos (IMHO), but if you just need a small office solution with a few machines and / or users and already have a Diskstation (RAID config and backup recommended) why not install a git server locally.
Install the git server as described in the Synology guide. Create users in DSM that match your workstation users and are assigned to the group Users. In git server DSM manager assign those users to git. Then use the following steps to create repos on the server (guide assumes
diskstation is your dns name of the Synology):
ssh admin@diskstation cd /volume1/Repos # that folder needs to be created within volume manager git init --bare --shared MyRepo.git
The option bare makes the repo a server representation of a git repository without a working directory and share makes the repo read/write enabled for all Users group members.
On your workstations you can than use the git ssh protocol to clone the created empty repos:
# if your local user and diskstation user match, clone as: git clone ssh://diskstation/volume1/Repos/MyRepo.git # if your local user and disk station user do not match, clone as: git clone ssh://your-user@diskstation/volume1/Repos/MyRepo.git
If you want to push your existing local git repos to the newly created diskstation counterparts use:
cd MyRepo git remote add origin ssh://diskstation/volume1/Repos/MyRepo.git git push --set-upstream origin master
After the set-upstream option you can omit it for further pushes.
You can save yourself from typing passwords and increase security by using ssh keys (copy your public key to the diskstation).