Alrighty, I've been meaning to do this for a while now and finally have the time (and coffee!).
Kayle is the most versatile champion in my opinion. She can support, top, mid, jungle or even ADC.
The items that I get with Kayle depend on the situation, but in terms of;
Bers Greaves, Malady, Trinity, Hexdrinker, Banshee's Veil, Force of Nature or Guardian Angel.
Bers Greaves, Zeal, Ininity Edge, Phantom Dancer, Blood Thirster, Last Whisper, and a survivability item, such as GA or Frozen Mallet.
This will give you a very high damage output and also survivability. One of the great things about Kayle is the utility of her skills, her heal speeds up movement, she has a slow, an AOE ranged ability, and finally her ultimate which lasts between 2-5 seconds depending on rank. It makes you invulnerable, though are still able to be CC'd (Like Tryndamere's ult but you can put it onto other people).
For support the game is a bit different. You're going to want to use your Q to buffer the enemy from your ADC while healing them up. So you need to run some high mana regen items. Tears of the Goddess will be your friend in this issue. Though for my full item build on support:
Faerie Charm/Meki Pendant, Wards and any pots you can grab>>>Philo, Boots (Sorc or Lucidity), Locket of Iron Solari, Shurelya's Reverie, ArchAngel's Staff, Guardian Angel, and a BV/Frozen Heart/Aegis.
When I get home I'll post more on this for runes/masteries.