What you are suggesting is what we call a credit card tour. KISS and just ride. All you gotta worry about is staying warm, dry and where's the next food/motel. Nothing wrong with that. Makes for easier miles for sure. A back pack would work, but a couple of small panniers would take a load off your shoulders.
I don't tour in cycling regalia, so can't help you with stuff you'd find in a local bike shop. I sure would hate to get caught out on the road in a cold rain wondering where the lbs was and hoping they had warm cycling clothes in my size. Best be prepared before you leave.
Clipless shoes are nice for on the bike. Little more efficient, but a tour is not a race. They are no fun to walk in, and you're off the bike much more than you're on it. Good pair of low quarter hiking shoes work just fine, or running shoes with a solid insert for additional padding.