My Personal Favorites (all categories)
So... this is basically just a list of my favorite champs based on their main or secondary roles (assassin, mage, support, etc.)
Mage:
or 
So, I have chosen Morgana and Zyra. Morgana is my go to girl for a mid-lane or a tanky magical support. Her Q can do upwards of 1000 damage as can her ult. Her W makes up for any lacking damage and her E makes her immune to all disables (that includes you blitz).
Zyra for the same reasons. Her flower turrets end enemies swiftly, and she doesn't need to land her powers to kill you. Zyra is my top lane, mid, or support character.
Assassin:
or 
Many people love Kat and Zed, as do I. These two work just like each other, they end enemies before they even know what is happening. So, that is really my main reason for liking these champs.
Tank:
or 
Garen is an overall tank. He can start or end fights. He is just an overall badass.
Leona is my favorite tank. The build I have for her destroys people in my favor. Once I get you in my sights game over. I have yet to loose with my build for Leona (granted I have only played it five times). Her stuns combined with brute force is a game over scenario for all players.
Support:
or 
Bard because Bard is cool. He has a great heal, powerful Q, and great escape tactics. Don't forget his life-saving ult.
Nami is so squishy but if you follow my build, she is a squishy tank. I did upwards of 1500 damage with ebb and flow once and then her bubble is around the 800-900 range. Her ult I believe was in the high 1000s. Her E is just to end your life with basic attacks (bonus of 200-300 magic damage). (Yes, I have done a mid lane Nami and won. I think it was against Zed?)
Marksman:
or 
Miss Fortune may be hot and she might be squishy, but don't underestimate her. She attacks from afar and can lunge right into a team fight with her ult. Possibly ending a few people as it goes. Don't try to run she always catches up (one way or another).
Gnar because well... cuteness becomes down right evil. He beat you to death with his boomerang and then smashes you to pieces with his mega self. Win-Lose for all champs (unless you catch this slippery yordel).
Fighter:
or 
I know Ezreal is not a fighter, but when I build him he should be. You cannot catch this guy and when you do he kills you (much like a Teemo). Also, don't run, his ult will get you (unless you're Yi, your heal blocks everything basically).
Talon is a fighter and can ends lives quickly and with little bloodshed on your part. Once he has you down low, your life is his. Kiss your perfect kill-streak goodbye or prepare to feed. Either way, he is tough.
My tactics (read this if you want):
Morgana:
I.F. (Item Focus): AP
Max Powers as followed: Q, W, E and then always R when available.
Combos: Q, W or E, R another quick Q, W if he enemies don't die.
Note: Choose between E and W. E will give you a shield and disable immunity. Her W is mainly used to deal damage that her Q is lacking for a kill.
Zyra:
I.F.: AP
Max Powers: Q, W, E. R always when available (this is for all champs).
Combos (cast always need seeds): Q or E, use W to summon more seeds. Use her R when surrounded by a lot of plants. Note, Zyra's basic attack will direct her turrets, so be careful.
Kat:
I.F.: AP
Max: I believe you max her Q, E, then W? I forgot which power was which. Max the power Shunpo last.
Combos: These are literally just a Q, W, E pattern. Use her R when entering a large group of people. Instant triple kill if your lucky.
Tip: Shunpo can be used to teleport out of fights quickly if you click on a moving ally or minion.
Zed:
I.F. : AD
Max: Q, E, W.
Combos: W, E or Q. When using ult: R-Q-E (you don't need to use W because it automatically turns on when hitting R).
Tip: Your W can allow you to escape fights, much like Kat.
Garen: Yea, I cannot go into detail about Garen. I have only played him a few times, so I will report Garen when I have more knowledge. Sorry!
Leona: This is my girl.
I.F. : AD (I know weird because her powers are magical, but trust me on this).
Max: W-Q-E
Combos: W-E-Q (this is my stun assault move) W-Q-E (up close and personal attack) Use her R to stop fleeing enemies or to finish them off if your E cannot reach them.
Tip: Leona can become tanky, but try to avoid 3-1 4-1 5-1 because Leona builds are squishy. Sometimes you can survive a 2-1 (90% of the time).
Bard:
I.F. : AP (not the support items, I never grab those).
Max (varies): If you want to be Bard that trashes people do this: (grab meeps always and foremost, but also max Q, W, E in that order).
A massive healer Bard is as followed: W, Q, E in that order.
R: Use this to keep your team from dying from last hit attacks namely Lux's ult, Ezreal's ult, turret attacks, and so on. Avoid using it when your teammate is firing their ult, their ult will miss.
Note: try waiting 10 seconds before using a shrine, their heal deals more if you wait. Also, hide them under turrets to avoid the enemy team smashing them (it won't heal them).
Nami: Love this champ
I.F. : AP
Max:
Support Nami: W, E, Q
Top/Mid Nami: Q, W, E
Tips: you do not need your Q to land, her W does a lot of damage. Also, if fighting Kat or Zed bubble them when they get close. Her E can be used to escape fights or chase people down, useful to land that final W.
Miss Fortune/ Gnar
I.F. : AD (both of them)
Max:
MF: Q, E, W
Gnar: Q, E or W. This is really your choice.
Tips: None for Gnar, still really knew. MF, if you can try to use her Q to finish off weak enemies (the weaker one should be your target). Her W can be used to chase down people and put more bullets into them. E can be used to ensure people cannot leave your ult or retreat from you. If they use a flash, you're S.O.L. You can cancel your R early if you want to retreat back or chase them down.
Talon:
I.F. : AD (I think)
Max: Q, W, E or you could do Q, E, W
Combos: You can choose. Mine is Q, E, W if I want to get close. Or just a W if I am retreating or want to stay ranged.
Use your R to either retreat or finish off some enemies (if low on health, also use it after activating your E, your ult will do more damage to at least one person).
Tip: Your Q deals damage to towers, so use it!
Ezreal:
I.F. : I think his is AP? Not sure.
Combos: E, Q, W - Q, W, E
Your E is used so that you can get close to enemies, but it can be used to escape as well. Fire your Q and W in rapidly within seconds of each other. It will do a lot of damage.
Use your R to wrap up any fleeing enemies.
Dream Team:
Top Lane: 
Mid Lane: 
JG: 
Bot Lane:
& 