engage champs, if you go top or jungle if you can play them, go maplh top, ammumu jungle etc you can just ult into the enemies faces and they don't know how to deal with the engage and probably will not flash in time either combo it with your E you'll eliminate a squishy or 3 at once.
if on maplh you build AP tank with HP and armour/MR depending on the team your fighting, use ludacity boots and your ult will have a 60s CD timer, use it every minute to shove everything into their faces.
seriously its the easiest way to win - on the other hand you can go very fast pushers like Quinn, TF, Trundle (destroys turrets) and simply push and push just take turrets, screw the kills screw the dragon take turrets when you can as fast as you can, before you know it you'll have so much map presence the enemy cannot get out of base, atleast not very far.
by ignore, i mean if you not close and a fight starts do NOT try to help, push instead, take the enemy jungle even this denies the enemy jungle serious experience and you can really slow down the snowball, if you can get in and you know you can either turn the fight or end it out right or survive and get out yourself while saving 1/2 others, take it but play it smartly.
any champ works though it really does it depends on play style and what you want to do or what you want to achieve or what your best at, but as a rule anything with a team fight presence is best so annie, organa, ammumu, maplh, maokai etc etc all powerful in fights and can usually end them