Office 365 is definitely the way to go in your situation (particularly since you need Access). Same software, just different licensing.
To get Access with Office 2013, you need the Professional package which is $400.
The cheapest 365 (home and student) still comes with Access AND includes licensing for 5PCs plus separate tablet licenses. For $10/month.
365 also includes some MS cloud extras you don't get with 2013. (I would never specifically pay for OneDrive service when there's Dropbox or Google Drive plus insync as superior alternatives, but I also don't complain about "free" built-in storage space.)
I think the one potential caveat is this:
You pay for Office 2013 once and can use it forever.
You pay for Office 365 as you go, potentially forever.
But, even then, at $10/month vs $400 PER LICENSE, it'd take a long damn time before 2013 becomes the cheaper option.
The best route is to install Ubuntu and Libreoffice and stop forking over money to the world's most determinedly-wrong software giant. Microsofts UX decisions just keep getting more batsh@t, and that crap carries over to Office, too.

"Modern" is the worst idea in the history of the GUI. It makes Android 1.5 look progressive.
What's hilarious to me is that MS Still charges $100 for an Outlook 2013 license. HOLY CRAP. There are so many (superior!) free alternatives out there...who the Hell still uses Outlook (even at work!)???