I generally do not suggest buying instruments online, sight unseen, untested, and without the backing of a store who will see to repairs, warranties, and such. I teach beginner wind players, and all my students who have bought online have had serious problems with their instruments that eventually resulted in their needing to buy or rent the better quality instrument at the local music store that can vouch for it. The best thing is to ask your teacher not just what the best brand is for you, but which store is the best to go to for your needs.
There are several music stores near me. There are a couple I tell people to stay away from all together, one that is better for winds/percussion needs, one better for strings, and yet another better for guitar-related needs. I also know which stores to recommend for repairs because I know they are fair, honest, do a decent job, and provide great customer service.
When you are starting out on an instrument, your local store is going to be much more helpful than any company online. The same is true when you are looking for mouthpieces. You should try out several. A local store can get a bunch in and you can go to the store and try them all there on the same day, and the only one you have to pay for is the one you buy. Or, alternatively, buy a bunch online to try at home and then spend all that money returning the ones you don't want.