Michael is correct in pointing out the incredible responsibility you'll be taking on. Mainly you'll need patience and self reliance. Let's start with your question about gas cost. Your trip is 4000 miles minimum, so let's assume 20 mpg and $4.50/gal for gas. That would mean you'd need at least $900 just for the drive. You should be able to do that yourself using your own values for mileage and our Fuel Cost Calculator in the left column of this page. You'll also need around $25/day/person for food or another $2200 for the three of you for a month. So we're over $3000 and you haven't done anything or stayed anywhere yet. Now it's possible to keep expenses low but a trip of this duration will set you back a bit.

Three weeks is about right for the trip you have in mind, but I tend to agree with Michael, that it may be a bit much as a first trip, especially with three of you. There will be inevitable conflicts as you go through day after day in close proximity unable to get your own way more than a third of the time. Hostels are fairly few in the US, so you will also need to do some research on any that are available on your route. Now is not the time to be deciding what to see and do but to scope out whether you can really handle it both financially and personally. That's a decision only you can make. You've come to one of the best places to get information on this sort of decision, but we can't make it for you and you'll need to ask a lot more questions before you can make it happen.

AZBuck