I ordered "Cox Internet Essential 30" which was $39.99 but they somehow changed it to Ultimate and charged $79.99 which I haven't requested.

Ok seriously, I will do everything I can to switch AWAY from Cox.  I have similar experiences as yours.  I was told one rate, confirmed it, then later when the bill comes it's a completely different rate.  I call in to see what was going on and I was told that they could not honor that initial rate.  "The lowest [they] could go was ."  Furthermore, this "new" lowest rate they could go would not be applicable to the bill that was sent to me because in essence - too bad, so sad, that was last month's bill and the "new" rate would only apply to future rates. 

Allow me to sum it up:

(1) Was promised $40.95/month (including tax) by an agent of Cox. 

(2) Received bill for twice that. 

(3) Told me the lowest they could go is $53/month.

(4) Was told that the bill for the month remains the same.  Because the $53/month was applicable to future bills, and not the current bill.

Are you kidding me?  I don't care what you call your plans - "no contract" B.S.  Cox, please consult with your legal team.  A contract need not be in writing.  It would not be smart of me to spend the $50 dollar filing fee to file a complaint against you and having to take the time out of my day to serve your registered agent with service of process, but heck, I'm starting to get mad enough where I am seriously considering doing so to prove a point.