$.99 will buy you a good burger, but you'll have to buy at least two of them ($1.98 worth, plus tax at 8.1% in Maricopa County) in order to become full.
Best bets: Burger King Whopper Junior (adding cheese incurs an additional $.10 charge, but can make the difference - recall my fondness for American cheese), Wendy's double stack, or Wendy's Jr Bacon Cheeseburger.
If you like mayo and fried conglomerates of coagulated chicken parts, McD's has a good spicy chicken sandwich (although the lettuce they use leaves much to be desired) and Wendy's has a similar option. Sadly, no one offers a good grilled option for $.99 that I'm aware of.
If you must kill yourselves slowly with trans fats, at least enjoy what you're eating. Happy hunting.