Hi! I'm glad to hear that distance is respectable. It sure feels like a lot to me!
Here is where my newbie news comes out - I don't know what sort of tires I have presently. The tires on my bike are the ones it came with - and I'm not sure what they are. They're not super skinny and they are pretty well treaded. They are sturdy too - the roads I ride on are rough and potholed and I've not had a puncture. At one bike shop they showed me a Jamis Explorer 2 and a Trail DX - my tires are bigger and thinner than what comes standard on those bikes.