You actually would not need to purchase a SD card, if you don't already have one.
The simplest and quickest ways to back up the personal data (photos, videos, music, contacts, etc., not apps) is to either 1. Save them all to a google account, 2. Save them to a cloud account or 3. Save them to a computer.
NOTE: Before you delete them off your phone, check the account and/or computer to make sure they are actually there.
To save to a google or cloud account you can send them directly from the phone, although depending on the place, it may take a while.
To save them to a computer, connect the phone via USB cord to the computer. Create a blank folder and move all the files you want to save over to the computer.
When you are all done with the reset of the phone, then download the files from the google or cloud account, or copy them back over (via USB cord) to the phone from the computer.