Simply put, you just need to make sure whatever car you rent includes unlimited mileage. As long as that is in your contract, then it doesn't matter if you drive 8 miles of 8 thousand.

The other thing you'll have to make sure is that your contract allows you to travel to everywhere you plan to go - 48 states would be the most common for your situation. Its not uncommon to see a limit of your renting state and the surrounding ones, so that's an important one to check.

Otherwise, you really don't need to think of this as a cross country rental, because you are doing a round trip. The logistics of your rental really aren't any different than if you were just planning to use it to drive around town for 3 weeks.

Insurance, if you don't have a personal car insurance policy already, it would likely be easiest to deal with the rental car company directly. Otherwise, you should look at companies that provide travel insurance and other policies specific to rental cars. A regular personal car insurance policy is going to be sold in a 6 month or a year long term, so its not what you want anyway. Crossing state lines shouldn't be an issue, as long as you are driving within the terms of your rental car agreement.

Costs are so variable its really hard to say, but if I was going to put a ball park number out, $300 a week sounds about right for an average car. However, you really just need to shop around to the various sites and get a feel of that for yourself.