There are very few champions that are just plain garbage. I think people noticed that when Nemesis Draft came out and no matter which champion you gave to your enemies, they could still screw you up if they knew how to play it.
From the Starter Pack: *Sivir is considered one of the best ADCs right now, very "meta" pick.
*Annie is also a very contested mid laner and support in the competitive scene and SoloQ.
*Nunu is quite effective if you learn how to play him since no one knows how to deal with counter jungling in lower elos (he's seen some competitive play this season)
*Ryze, Master Yi and Kayle are late game monsters and can easily carry in lower elos where games will go past the 40 minute mark almost everytime.
From the Champions bundle:
*Sion is a strong lane bully, while also being very tanky and scaling into late game. Very solid pick for top lane, although he will probably be receiving some nerfs in the upcoming patches (mana cost on E).
*Corki is an extremely bursty ADC with arguably the best mid game amongst them all.
*Twitch is one of my favorite champions, overall an A tier ADC that was also a favorite pick at Worlds by the top teams (SSW, SSB, SHRC, etc.). I find him to be very strong in lower elo since although his early game is considered weak, people there can be clueless sometimes and get baited into having an extended trade with you, which you'll win because of your passive and E. Even if you don't get some cheesy first bloods, his late game is brutal and overall his assassin-like playstyle is very effective in Solo Queue (the unseen rat is the deadliest).
*Anivia, Katarina, Jax are good picks if you like to blow people up.
*Singed is awesome. I think he's one of the hardest champions in the game since you have to play a psychological game and bait your regular SoloQ morons into doing stupid things like chasing you. I especially love his proxy farming playstyle that lures your own teammates into thinking that you're trolling. There are a lot of excellent guides (eg. InvertedComposer's) if you want to ruin the day of everyone and also get some easy LP.
*Heimerdinger. This fucking guy. No one in low elo knows how to play vs him, and he's such a brain dead champion. Easiest way to Gold, just ban Syndra and watch the LP flow in.