I found these useful articles about using a network share with Apple Time Machine (Apples built-in backup feature).
Using a Network Share for Apple Time Machine
There appears to be some issues with using a network share once it runs out of space, as the backups are not pruned correctly from what I can tell from the posts. There is a post on the firrst link that says the issue has been resolved with a recent Time Machine update, but not for sure if that’s the case. I haven’t tried it myself yet (not that brave yet 😉 ) plus I have an external drive that I use for backups anyway..
Here’s also a nice article on tweaking Time Machine:
And here’s a link to a Time Machine alternative (includes a comparison chart too):