Hey Nate, don't know if this is too late, but here's acouple of brief pointers.
I also toyed with the idea of taking a tent and camping out.
Taking a tent and camping out is, I found, one of the best ways to go, if you're looking for cheaper accomodations/an alternative way to sleep if you find yourself caught by darkness on your tour. Make sure you're you're familiar with camping though. If you haven't yet done a camping weekend, do one with your tent and your girlfriend, and study up on the subject of waterproofing your tent, bringing foam sleep mats etc. The devil's in bringing necessary camping equipment without overpacking for it. Remember, you're paying for convienience by hauling that extra weight of equipment around.
How do you then prepare your route and find places to rest?
Depends on where I am: big city or countryside? Big cities generally mean you'll be travelling through suburbian hell trying to get out. I don't enjoy it, and if I have to enter or exit a city I take a local train to just beyond city limits. Make sure you ask a local where the countryside really begins. In the country, you can often obtain local maps of surrounding roads. These are super-useful, and often free at campgrounds or hostels. Ask tourist offices in the little towns or campgrounds about biking routes. They can be extensive even where they're not widely advertised. Give yourself at LEAST an hour before sunset to get wehre you want to be and set up camp. It's nicer find a place to eat and sleep while it's still light out.
How do you carry your equipment?
Equipment is usually carried in panniers or trailers. Do a search through these forums for info on each, and the pro's and cons etc.
How much would you expect a tour of this short length to cost, both financially and physically?
I'm fine with cycling long distances, I can easily keep up a week of 40 - 45 miles per day around my home area, but I was wondering if this has any translation in cycling in a completely different country/environment.
You should be fine physically. Keep in mind that you're just starting out, depending on your legs to get you where you need to go. Give yourself rest days where you don't even look at the bike, listen to your body, respond when it complains about water, food, aches and pains.
best of luck, and let us know how it turns out!