Welcome to the RTA Forum!

You mention both the southeast and southwest as your destinations, so lets start with some specifics on where it is you know you want to go for sure? If you did mean southwest, and you've got 2-3 weeks, you should know that it takes about a week to drive across country, so for a round trip, you'd really want to be on the upper end of your time frame.

As far as a car goes, I would not purchase a car with only a roadtrip in mind. Its just too big of a financial purchase to be one dimensional. Look for a car that will be comfortable for your trip, but that will also be practical for your needs after the trip. Buying a minivan with the hopes of sleeping in it (which may not be all that comfortable for 2 people) and then being stuck with a vehicle when you get home that doesn't meet your need could easily end up costing you far more than just staying in motels.