The battery will cost about $90 plus tax (U.S.)
Make an appointment at the Apple Store or take the phone to an authorized Apple service shop....(appointment not needed)..... for the battery replacement. The shop will check out the phone and clean it up as well.
You can find a list of authorized service shops in your area using this link: Find Locations
You might consider replacing the screen protector on the phone, or adding one if the phone does not have one at this time.
Follow the instructions in the Apple Support document linked below very carefully, to insure that the phone is set up correctly for a new person. The repair shop can help with this as well.
What to do before you sell, give away, or trade in your ...Apple SupportOfficial Apple Support › en-us
Good luck.