My dentist told me not to whiten DD's teeth until she is 16. She also told me not to let her use the whitening toothpaste. I would check with your dentist.
My dd15 wanted to whiten her teeth after her braces were taken off and our dentist said she doesn't usually bleach kids until 16 - but, because dd's teeth were so stained, she agreed. We went with custom made bleaching trays because they keep the bleaching material off the gums (as much as possible). Total cost was $199.
I purchased the premium Crest strips from a previous dentist for $75 and used 1/2 of them before I simply couldn't stand the pain anymore caused by the bleaching. Tooth shocks, gums were tender, etc. But, my teeth were whiter. I've never been able to use the rest because the memory of the pain is still too fresh - 2 years later.
Regardless of what you choose, ACT flouride rinse is recommended by dd's dentist to help with sensitivity issues caused from whitening.
Arm & Hammer toothpaste works great - but, so will dipping a toothbrush in plain baking soda. Unfortunately, baking soda (and whitening toothpaste) is abrasive and if one brushes "hard" or uses a hard/medium bristle toothbrush, it is possible to brush away enamel and cause grooves in your teeth. Same problem occurs with Sensodyne (any "sensitive" teeth toothpaste). I speak from personal experience and from what dentists have told me over the years.
This is a bit "OT" but, since we are talking about teeth, I want to warn parents with kids who have braces or are going to get them about what some orthodontists do to make space for a perfect smile. My dd saw 4 orthodontists before all was said and done and the braces came off. The last one (young & fresh out of school) said he could file off the sides of dd's teeth to make them fit better. I was SHOCKED! He told me it is "quite common practice to file the sides of teeth."
I'd had a military dentist do this to one side of one of my front teeth years ago and I've had nerve sensitivity with this tooth ever since. I didn't know what the dentist was doing would screw up my tooth forever or I'd stopped him in his tracks! I can't imagine an orthodontist would recommmend this to make a perfect smile. DD was only about 6mos from completion and I had already signed a contract with the guy - otherwise, we would have found somebody else. I went with her to every visit and I sat in the room to observe what he did. I wanted to ensure he did no filing. Please don't allow this to be done to your kids' teeth.