If you want a sub-$100 bike, then go to walmart and buy the most expensive bike that is less than $100. If you have a choice between a bike with suspension and one without for about the same price, get the one without. The simpler the bike design, the better the parts are likely to be at a given price.
Get a 26 inch wheel bike. A 24 inch wheel will be way to small for you. You may have trouble finding a 26 inch wheel bike that fits since most of the cheap bikes are sold for kids.
If you could go up to $250 you could look at something like a Dahon Boardwalk 6 folding bike. That would easily fit in your trunk, on a bus, train, or in a suitcase to be checked as airplane luggage. Just a thought.