First off: where do you find connections to the internet, and how much do the connections cost per minute?
Airports charge substantially. Hotels may charge, and I've found no correlation between the cost of the hotel and the availability of included internet service. (I don't stay in hotels very often though.)
Best bet imho is coffee shops. Starbucks has a contract with, I believe AT&T. You can buy an hour for a couple bucks or, I believe, you can pay monthly for service.
Second: can a decent laptop be found used for not a lot of money and, if so, what would be a good brand and model?
I'm a diehard Apple fan, but after durability problems with the construction of two out of two of their low-end laptops, I no longer think that the thousand dollar mac is a good option. Probably you weren't even considering Mac, but still, I've had noting but great luck with other mac products, and terrible luck twice with low end laptops from them.
Third: would a laptop survive in the touring bag on a vibrating Harley?
It kinda throws out any possibility of real cheap, but do some research into solid-state hard drives. The new MacBook Air is available with one for the low, low price of $3100. I don't know about PC versions, but I'm sure they are out there. Allegedly much more resistant to vibration and other physical stresses.