AP: Lux - gr8 range and cc + shield and a low cd sniping ult. All abilities are skill shots though.
Gragas - Good range and aoe skills (Q/R), has a sort of escape/slow, ult dispaces the enemy team if used right but can backfire on you and hes sort of tanky. Fun champ. hes melee tho.
Le-blanc - Good early/mid game presence and good 1v1 dmg but relatively useless as the game progresses and in team fights.
Karthas - gr8 late game champ but might seem lacking dmg in the first few lvs, has free mana regen. you need to land you Qs and ult at the right time.
Mordekeiser - melee champ, if i recall right hes bad early game but can be hard to kill if he gets fed.
Kassadin - Anti ap assasin with built in escape [ult]. youl need to b able to farm without dieing in early lvls though. [melee champ]
AD: Gangplank - Has a free get out of jail card (it heals and removes cc etc), his Q can get you some extra gold, has ad/as/ms passive/active steroid, ult is global, Dot/slow passive. [melee]
Xin'zhao - Can jungle or top lane, has inbuilt armor pen passive, has a gap closer + slow, knock up on Q and knock back on R, has in built sustain and AS steroid. [melee]
Pantheon - Can jungle and lane, has a stun and passive is useful as it can block turret hits if i recall correctly, 100% crit on low health target. ult can be used to escape/get to a fight but chances of landing the dmg on players is low. falls off late game.[melee]. PS i dont play him much so idk how easy/fun he is.
Olaf - Q has slow and get reduced CD if you get the axe, has inbuilt sustain (spellvamp+lifesteel), he gets more as low health he has, does true dmg, ult makes him even more tanky and immune to CC. Gr8 champ in lane or jungle, easy to use and i would recommend getting him. [melee]
Corki - Good ADC, does a bit of true dmg on attacks, has an armor shred on 1 ability, has a good escape though with high CD, Ult has good range for poking on decent dmg. [Ranged]
Twitch - I wont comment on the effects of the remake especially since I didn't play him till after. Has stealth and AS steroid on Q, has an aoe slow on venom cask, Dot passive which stacks 5 times, can do good dmg early on with 5 stacks of poison + expunge, ult increases range and dmg but needs good positioning. [Ranged]
Oddballs: Akali - Good burst dmg, has a good gap closer once you reach lvl 6, has a aoe 'stealth+slow', to make her 100% effective you need a rune page for her. not recommended till you get lv20 runes. Can pubstomp easily. [AP melee]
Nidalee - Can be built AP/AD/support/hybrid, her Q in human form does more dmg longer it travels but is a skill shot, her heal also gives AS, her trap reduces enemy defense stats. Has no real 'ult', her Ult changes her to cougar form giving a little extra armour/MR. her Q in cougar can act like a finishing blow as it does more dmg based on health missing, get a mini gap closer, spells in cougar form cost no mana. AD tends to make her tankier than AP build and uses her cougar form for dmg. AP makes better use of her Q better and all her spell excluding cougar form Q scales with it. AP is squishy so if you get caught you can die easily. [Human form - ranged, Cougar form - melee]
Hope this helps. Most of are good characters, try em in free week before you buy. Gl and hf.
PS sry bout any mistakes in this, not slept tonight so rather drowsy atm.