My #1 FAVORITE tea company is TEAVANA!!! Hands down it is my favorite. It is pricey, but I think it is worth it.
Now in no particular order are my next favorite tea companies....
Twinings is classic company that has been around forever! The have bagged tea as well as loose tea. They are one of the few companies that I do like their bagged tea even though it is not in a mesh bag. Their tea has great flavor.
I know that there are hundreds of teas out there and so many choices you can make, I hope this helps you in narrowing down some decisions! None of these tea companies pay me or give me kick backs- so these are just my honest thoughts in effort to help you. You are on your own picking flavors. That is always a personal thing. Me, I like green but really only in Jasmine tea. I am not a fan of white. I am hit or miss with Mate teas and Rooibos teas. I like black tea with milk and I like a lot of herbal.