if you're going top, play an 'assassin' (burst damage champ), fighter, or carry with high mobility--blinks, dashes, and in some cases movement speed steroids.
if you're going bot, play an extremely strong 1v1 laner. ability to push, kite, sustain, and kill are all important. also, it's strongly advised that you take a champion that scales well with gold.
examples of good champs:
top--kassassdin, leblanc, talon, fizz, shaco (ad), pantheon, wukong, riven, poppy, vayne, graves, and caitlyn.
bot--yorick, ryze, cassi, jarvin, heimer, urgot, and maokai.
note that the mage and carry champs i listed can pretty much go top or bot without issue.
edit: also, i don't really think that any champions are bad picks (unless they're not needed for the team comp). you can do well with pretty much anyone if you build/play them properly for the map. i just listed the more popular champs for each starting role.