Don't go crazy and spend a ton of money until you find out if you even like the quilting process. Since you want to quilt with your daughter, maybe starting with a doll quilt would be a good idea.
Buy a medium sized cutting mat, ruler and rotary cutter. Pick a few fabrics you like and start with a simple pattern. 4-patch or 9-patch might be good.
If you are really a beginner sewer, you might even want to start with pillowcases. They are very easy and statisfying to make.
Look at Missouri Star Quilt Company for videos ideas. They explain things very well.