Kayle was one of the first Champions I bought in the game. I loved the fact that she was an angel and seemed relatively easy to play.
She appealed to me because I play an angel deck in Magic the Gathering and she somewhat reminded me of Gisela, a pretty badass angel. Her abilities are Righteous Fury, Divine Blessing, Reckoning and (her ultimate) Intervention. I recommend you choose Fury, Reckoning, Divine blessing, Fury, Intervention then Reckoning (that'll get you to level 6, from then on you should max Fury and Divine blessing, whilst taking Intervention whenever possible).
Righteous Fury- this ability increases Kayle's attack range, as well as dealing 20 magic damage on hit and 25% of her attack damage and 30 magic damage on attack- it's pretty badass.
Divine Blessing- this increases an ally's movement speed by 18% for 3 seconds as well as healing them fro 60hp.
Reckoning- This blasts a target, dealing magic damage and slowing their movement speed by 35%. While they're slowed, Kayle inflicts bonus damage to the target.
Intervention- This makes Kayle's target immune to all damage for 2 seconds.
I tend to go for Attack Damage when building Kayle. Obviously, you start off with 3 health potions and the Boots of Speed, but you should then save up for a BF sword which should be built into a Bloodthirster. The shoes I tend to build into are the Ionian boots of Lucidity, as they decrease cooldown as well as increasing movement speed.
Overall, Kayle is a really fun champion to play as and I advise you to give her a go- she's also cheap to buy!