Switching contact lenses?

Ok so I just got my contacts on Tuesday.I have never worn contacts before.So my question is when I order contact lenses on 1-800 Contacts or any other contact place can I choose any contact brand?I am currenly using the AVAIRA contact brand.That's what the eye doctor gave me.So can I just order any brand of contacts like Acuvue or FreshLooks when ordering contacts or should I stay with the brand my eye doctor gave me?Would it hurt my eyes to switch to another contact brand?My contacts don't run our for a long time.I have two different prescriptions for each eye.The eye people gave me a trial pair and then I bought two boxes of contacts while I was there.They didn't have my right eye contact box so they have to order them.I do have a box full of my left eye contacts that they gave me.I am using the right eye trial pair contact lens,which is only one contact lens.I have a box full of my left eye contact lenses.The brand they gave me is AVAIRA for both my eyes.