Can I use GitHub to edit my Project on both my Mac and PC?

I am a mac user and use my Adobe products, etc all on my Mac. I recently got a PC in order to use the HTC Vive. I want to primarily edit my Unity project on my Mac but also have the ability to make some quick edits on the PC version while I am testing the virtual environment.
I did some research and it sounds like the best way to collaborate between two computers it GitHub. I'm wondering if this is the best way to go to work between a Mac and PC. Also is it free to use with the free version of Unity (I am just learning the software and don't have the full version)?

 

ya git is the way to go but you can only store public projects on https://github.com if you wanna sore private repositories i recomnend https://bitbucket.org

the great github client (https://desktop.github.com/) works with all
- mac & windows
- private & public
- gitbut & bitbucket

 

*You can skip this first section and jump to my EDIT below, which seems to answer some of my original confusion*

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I saw that some users are saying BitBucket may not work well with Unity projects, do you think this will be an issue:


"I used to use Bitbucket too, but for what it's worth their terms of use make it pretty clear that the intended use is to store source code only. Large amounts of binary data are frowned upon and may result in repositories being deleted... which needless to say would suck."

"Yes, this happened to me. First they locked the repository so I couldn't push anything new to it, and then we had a chat - they agreed to let me stay if I took out one of their $15/mo subscription plans, which I did for a while.

In the past couple of weeks I've moved the project over to Unfuddle, who provide 50GB for $3/user/mo (with extra space at $1/mo)."


http://forum.unity3d.com/threads/how-to-collaborate-dropbox-just-broke-everything.262551/#post-1737637



EDIT: Clearly BitBucket should work because Unity recommends it on their own website! Perhaps the info I found was old. Unity has a (overly simple) how-to guide ( http://docs.unity3d.com/Manual/ContributingToUnity.html ) that uses BB. However a lot of the more in depth tutorials on Unity and version control that I see online are using GitHub instead. I believe the problem with Github is that if you use the free version, anyone can access your files and you have no privacy (correct?). It sounds like BitBucket is a different service that allows privacy for free and sounds like the way to go, just like you said.

Does BitBucket work with the free version of Unity? Or perhaps the Pro version has built in helpful workflow options, but you can always manually sync with a third client software like you mentioned.

Sorry for all the questions and confusion on this stuff and I appreciate your help!

EDIT 2: Okay it turns out that official Unity link wasn't for your projcects version control, it was for submitting ideas to change the Unity software itself (or something)! Now I'm back to being confused and am wondering if GitHub is the only way to do this