OK, just an opinion, but you need to make this real.
Cut the one month thing, it'll just take however long it takes.
All you need is a starting point. And a first destination.
After you make it to the first destination, you decide where to head next - this is where the locals can help out telling you what's near, and what you should go see/stay away from.
10K?? don't go into it on a budget. just go, and keep going until the money runs out.
Don't turn around and come back to the same place you launched. Make one of your buddies that stayed back drive your truck/trailer to wherever you wind up, and take your happy azzes back home.
Take a tent and sleeping bags, you may not always be able to find a room, and you'll just have to make do.
Make it a real adventure, IE just go do it with no real destination.
This isn't the sort of thing you use a travel agent for.
This is one of your last chances to be young and completely irresponsible - you better make it count.