How should I prepare my back ups before turning my Mac in for a battery replacement?

Before bringing it in for service backup everything. Make a Time Machine backup or a clone.

Back up your Mac with Time Machine - Apple Support

Replacing the battery shouldn't affect your data but it's always a good idea to have a backup as anything can happen.

Get your Mac ready for service - Apple Support

To add—

How to create a boot clone https://discussions.apple.com/docs/DOC-10081

You can google "3-2-1 backup strategy" for a bigger picture on a robust backup plan.