best way to set up an ipad for a child - do I use my parent apple ID?

Make sure that each family member has a unique Apple ID - Apple Support

If this is a minor child: Create an Apple ID for your child - Apple Support

Set up Family Sharing - Apple Support

Transferring ownership of purchases from one ID to another is not possible. You will have to Family Share past purchases. As for her playlists:

How to make a playlist in the Apple Music app --> https://support.apple.com/HT207542

"If you have a profile on Apple Music, you can make a playlist public so anyone can find it when they search Apple Music. When you create a new playlist, turn on Show on My Profile and in Search."

How to share music to Facebook, Instagram, or Snapchat on your iPhone, iPad, or Android device --> https://support.apple.com/HT211799

Also of interest: Approve what kids buy with Ask to Buy - Apple Support

Hi Melissa , you can set up your daughter iPad using family sharing and there you have the option share from your iPhone to your daughter iPad everything you want , if you have a Apple Music family subscription then she can access her playlist from the Apple Music app Apple TV app sucloud storage and more and in settings focus you can set up things that you don’t want her to get access, from family sharing she can’t download apps without your authorization either etc etc and yes she can have her own Apple ID account