i used 700x35 tyres, i could have used narrower as i was on proper A roads nearly all the way.Cycle paths at times i find a pain as you can lose direction, or miss a sign fairly easily.
Regarding people saying dump the weight, it isn't them who wil spend 2 weeks in the saddle so do what you feel is best, i took 4 panniers which was overkill, and really slowed me down, for all future trips i'll be taking the trailer that i am building.
I was wild camping every night for a full 3 week period, so i felt i really did need to have loads of stuff with me, i travelled solo too, and the nights were cold, it was the end of October.
Things like food from the supermarket, and 2 litre bottles of water could fill a pannier by themselves, you should be able to avoid that part as you have a place to sleep each night under a roof, whereas i didn't.
Insect repellent should come in handy.
How are you travelling back?Train fares are very low if booked in advance, you can do 400 to 500 miles for under £15 with bike reservation.