There's this $35 or so rider you can get on your home insurance that covers drain backups. I suggest you get it.
Putting things in plastic bins was a great idea
It's mostly rainwater that backed up, but not all (I know you were wondering)
When finishing a basement, two things to remember to prevent permanent flood damage:
1: Use treated studs as footers
2: Use at least three coats of polyurethane on "low" wood