I would send my daughter to a decent store so she could handle a bunch of different knives. She needs to find the most comfortable handle for herself, this is crucially important. It won't be a surprise gift, but there is a wide range of handle shapes out there any no one likes them all equally. The handle-to-hand fit is forever.
Modern steels are so good that most cooks don't need anything exotic, just good quality mid-range steel (or better if the wallet allows!).
The food you eat matters when choosing knives. The stock answer used to be 8" chef, 5" flexible boner and a 3 1/2" paring knife (and a big long serrated bread knife if you were going to buy four and couldn't sharpen any of them).
Folks used to eat more meat with bones and big birds in the olden days. The boner made sense when a light meal included a turkey or a big chicken. The flexi boner got plenty of use and it was a lot better suited to big boning tasks than the paring knife. Folks who don't eat a lot of meat with bones or big birds and fish would probably get more use out of a 5" utility/petty/santoku type blade than the flexi boner.
As to the long serrated bread knife, save your money by buying a couple of good diamond stones which you need anyway and keep the chef sharp. A sharp chef's knife slices any bread as well as a serrated knife. Hard, stale French bread, soft, fresh-out-of-the-oven bread, I can't think of a job that the sharp chef won't do as well as the serrated bread knife.
I have become convinced that the only reason the serrated bread knife exists is because people are so attached to their dull chef's knives! People love their dull chef's knives so much that they refuse to sharpen them! And since they are too dull to cut bread they need a serrated bread knife to make a sandwich! It all makes sense now! The dull knives are part of a grand, stupid plan!
You really should budget your sharpening tools up front as well, because you will start needing them almost from the beginning. A Sharpmaker is a good choice to get started, otherwise get a diamond stone or two and practice on beaters. Don't let your knives get too dull.
My personal preference would be a 7" santoku and a 3 1/2" or 4" paring knife, together with a steel or ceramic hone and eventually a couple of good diamond stones. Good but not necessarily the best quality stainless (for home use), and most importantly a handle that fits my wife's hand! After a few weeks of use I would know what additional blades she/I might want or need. Maybe the 5" santoku. The wide blade and greater knuckle clearance of the santoku works well for me. I can process some food with that blade shape, and use the back of the blade as a spatula. A well executed santoku is a formidable kitchen tool!