It depends on you and the state how you want to explore.I will suggest you to have sufficient time or divide in parts.There are end less places in each state.I would advise you for road trip.Hostels are cheaper but for a luxury stay Ten thousand pre day for one family
Depends on the no. of days you wanna spend there. But for a completely smooth and satisfying travel, I recommend give a year to it. It can cost you big bucks so better start saving up!