You may find that the toys she's most interested in are the least sophisticated. A metal mixing bowl and a plastic spool, a drawer full of GladWare, some plastic cups made into a pyramid and a ball can go a long way (even with my kids at 2 and 4).
Each kid is completely different. Our son has always been drawn to cars, trucks, very masculine toys. Our daughter is completely different.
As far as discipline, it's one of the few areas for which we don't agree with our pediatrician. I don't believe redirection is effective most of the time. I do personally believe it ignores the bad behavior and doesn't set expectations of what's acceptable.
Yes, I'm that disciplinarian mom who has high expectations of my children. I expect pleases, thank-you's, excuse me's, I'm sorry's, etc. I immediately correct my kids for things I hear and things I see and let them know, without reservation that it's not acceptable. And, my husband and I are always receiving compliments on how well-behaved they are at 2 and 4 years-old.
Hitting, biting, etc. you can easily correct with an authoritative voice and a simple, "No, we don't hit". After enough repetitions, you can ask them "Do we hit" and they can respond to make sure it's understood.
Becoming a toddler is all about exerting independence for them and keeping it in check for us. Unfortunately, I've realized lately that most parents don't want to be the bad guy, they want to be the friend and to be loved and adored. Because of the communication gap, one of the easiest ways we found to reduce frustrations was to ask them to "show me" what they needed.
Letting the behavior go will only create more problems down the road and make it more difficult to correct. One thing we all need to do more of is complimenting for what they do well and when they behave well instead of it all being correction.
My kids are certainly not angels, and we have joked (yes, only jokingly) about putting them on e-Bay on multiple occasions.
Good luck! It's all trial and error, and you're both learning here.