Cycling around is good fun. It's not the quickest way of traveling, but you earn every kilometre.
I really wouldn't recommend using whatever bike you happen to have - it's not designed for that. You need a touring bike or a "hybrid", something reasonably lightweight and comfortable, yet durable enough to carry a whole bunch of shit. Here's a good starting point:
https://en.wikipedia.org/wiki/Touring_bicycle and there are tons of sites out there made by people who've done epic cycling trips and are keen to tell everyone all about it.
If you start riding something not suitable or totally comfortable, you're going to be hating life after a few days and a few hundred kms. Plus, it'll break often. It's sometimes worth paying more for quality stuff, like double-walled tires and proper clip-in pedals and shoes.
Make sure you're protected from rain, sun and heat. Make sure you can repair any common issues like flats or broken chains. Do whatever you can to keep your ass from getting sore (it will anyway). Buy some good lights for your bike, and do whatever you can to make yourself visible to the driver who isn't paying attention.
I've never had any problems dragging my bike into the woods and leaving it next to my tent. Having good maps can keep you on quieter roads, making it much more fun and relaxed. Get a good lock and you'll be able to abandon the bike for a couple days when needed.
Anything else?