Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Start with Ruby Crystal. On the Lane, keep conservatively last shooting the creep by your righteous fury. you would get 850 golds around level 5-6 then recall and grab Catalyst of Protector and immediately teleport back to the lane and you will feel the power of Kayle. :]
for the rest of the items, I recommended the Damage Category because of the passive skill, Holy Fervor, but which specific one is better depends on the opponent team. For example, your target is the Tank with Warmog and Force of Nature, so you should probably get the Black clever to Benefit from their lower armor. Or against Enemy with High armor and Hp, Madred's Bloodrazor is the key.
To maximize Kayle capability, Mana management is the key. and To emphasize the skill, Righteous Fury, Attack speed is the main factor of damage output making her a bit early advantages.
Ghost is very all-round summoning spell in case of escaping, chasing, or regrouping. and Teleport is as well all-rounded but should be maximized enough to use because of the cooldown.