Personal buy order due to preferences. I am bad at assassins, much better at poke/high range/support champions. I favor tanks the most after those types.
Tops: Nidalee, Gragas, Shen, Olaf
Mids: Lux, Heimerdinger, Anivia, Karthus, Mordekaiser, Katarina, LeBlanc, Kassadin, Akali
ADCs: Corki, Miss Fortune, Twitch, Urgot
Supports: Karma, Blitzcrank, Sona
Junglers: Rammus, Pantheon, Shaco
Okay But Where Would You Actually Play Him Perhaps Top But Why Would You Do That: Gangplank
Now, the above is just based on my personal preference and doesn't actually imply 'good'. Also, I listed Pantheon as a jungler and Karma as a support and so forth but they're also viable top and mid respectively... and so forth.
Based on popular competitive picks as of late, you'd most likely go with:
Tops: Nidalee or Gragas.
Mids: Kassadin tends to be picked when not banned (not always). I've seen Lux a few times. Karthus a very, very occasional pick, largely for his ult. LeBlanc went on vacation after her silence was removed.
ADCs: Corki and Twitch both come up often.
Supports: Neither is picked particularly often lately, but Karma appears more often than Blitzcrank.
Junglers: None of the three are picked particularly often lately. Pantheon used to be a popular choice until changes to his ult.
Gangplank: No.
But if I had to tell you, generically, what to buy: go with what suits your playstyle best.
If you're an aggressive player who enjoys all-ins and 'oh hello i am here to kill you' style plays: Nidalee, Katarina, LeBlanc, Kassadin, Akali, Twitch (invisibly sneaking up on folks), Blitzcrank (can't solo but can pull so that someone else can be like 'oh hello oh goodbye'). Shaco maybe possibly but I just really hate clowns okay. Also, Karthus is basically "let me just go throw myself at the enemy so I can die while dealing tons of damage" so while he is nowhere near similar to the others he needs to be in the middle of the action to be effective.
If you like to play a little safer but still like being a damage dealer: Lux, Heimerdinger, Karma (all three excellent pokers, Lux has good burst and very high range), Corki (has a good escape built into his kit).
If you like to build tanky/utility and act as a front liner or just generally assist your teammates: Gragas (can also be built for damage but has been more effective tanky), Shen, Rammus.
I don't know enough about Olaf, Anivia, Mordekaiser, Urgot or Pantheon to really place them anywhere in particular or tell you much about their play style. I played Morde once against bots, walked out something like 30/1, and many laughs were had. I own Pantheon strictly because I got his Dragonslayer skin code.
I wouldn't buy Sona just yet as she's just been reworked and tweaks may be incoming.
Miss Fortune... I like her, but she's in a bit of a peculiar spot as an ADC at the moment in that there are others who can deal the same damage she can while having better escape mechanics. And Gangplank, well, let's not talk about Gangplank.
Aaaand I wrote a book.