So the whole point of this guide is to max out the power of kayle's abilities, focusing on her ability - righteous fury- set on the E key.
If you haven't ever played as Kayle then the abilities effect will be briefly explained at the Skill Sequence section.

NOTE. There is no right or wrong way to play a character and this is what I think is the most efficient way of playing one of my favorite champions, Kayle.

I chose the spells Ghost and Flash for a certain reason. Flash,teleporting to your cursor's location instantly. Even though it has a ridiculously long cooldown it is really useful for picking up a kill or escaping a gank.
Same thing goes for Ghost, increasing your movement speed by I think it's around 25% for about fifteen (15) seconds. Although this is more efficient if you need to rush to the edge of your lane or just move quickly.

Alternatives

I guess it would make sense to use Ignite (dealing damage depending on level for 5 seconds) instead of Ghost. Or perhaps Promote for that extra force in your minion wave if you are to take down an enemy tower. (Again this is my thoughts and it's totally fine to disagree)
Although i see no direct use in having Heal or Exhaust since Kayle's abilities (See next chapter) both contains a slow and a heal. Also with spirit visage boosting all self healing processes (lifesteal, spell vamp, healing abilities and health regen. by 10%) you should be able to do just fine without the heal ability.
The surge ability giving you increased ability power and attack speed would make sense to use too but again since almost the whole item purchase is based on those two it's not something you can't live without.

As I mentioned before the idea of this guide is to customize runes and masteries to bring out the full power of Kayle's ability bound to the E key, righeous fury.
If you never played Kayle, here's a brief summary of her abilities

Q: Reckoning: Kayle fires a red blast against a targeted enemy unit (no structures).
This slows the enemy unit and deals damage. This ability stacks on both Attack damage and Ability power. Making Guinsoo's rageblade a great choice.

W: Divine blessing: Kayle heals an allied champion or herself. This ability also raises the movementspeed of the target by about 20% for 4 seconds. The number of healthpoints increase depending on how much AP Kayle has, therefore Nashor's tooth, malady and guinsoo's rageblade + the AP in the runes makes this ability do.. alot. (Also spirit visage makes this effect 10% better when kayle heals herself)

E: Righteous fury: Kayle's basic attacks gain 400 range (about as much as tower-range).
Her attacks also deal bonus magic damage as well as splash damage (an AoE effect around the primary target dealing about 20-60% of the damage) The reason I stack this attack on AP instead of AD is because I wan't the splash damage to deal as much damage as possible too.

R: Intervention: Kayle selects an allied champion which then is shielded from all damage for 2-3 seconds. When I first started playing Kayle i thought that this ability was quite useless since it's only 2 seconds. Then I learned to time it correctly and it's just awesome! 2 seconds is enough to for example shield almost completely from fiora using her ulti. Also when upgraded to lvl 3 it only has 60seconds cooldown without any cooldown reduction. However, since both Nashor's tooth and spirit visage offers cooldown reduction it's reduced by quite a bit. Wonderful!

Now, let's go back on topic, when to upgrade what skill?
Since I already said a number of times that I'm maxing out on righeous fury, use that as a first skill. It allows you to get a good shot at your opponent or just to farm from a distance. (if minions move in a group, try to target the middle one allowing the splash damage to damage other minions simultaneously). In lvl 2 pick Divine blessing, the heal.
This allows you to lane a little longer, recovering lost health or if getting chased a slight heal + some movement speed to outrun your enemies.
At lvl 3, continue with the righeous fury since you won't need the slowing effect unless you're going for kills. In early game it's better to go for harassing and farming minions, make sure not to take down any tower for a unnoticed advantage. If you score in kill after kill you will surely be ganked.
See the Skill sequence table above for further guiding.

I usually start off with the amp. tome without any pots in case you'd need those extra 35 gold later. After that purchase a meki's pendant and upgrade to fiendish codex. I think it's good to buy boots of speed before upgrading fiendish codex to nashor's tooth because it gives that extra movementspeed which you will need to escape ganks and get back to your lane as soon as possible. After that finish up your nashor's tooth by purchasing a dagger followed by another dagger, followed by upgrading these to the "stinger" and finally nashor's tooth.
Keep on building your offence by buying an amp. tome and two daggers, upgrading these to the Malady.
At this point it depends mostly on how you are doing in the game what to build first. Although i'd strongly reccomend getting guinsoo's rageblade gaining you more ability power and attackspeed the more times you attack or the spirit visage first.
If you're feeling kind of like you're having a hard time staying alive then definitely go for the spirit visage first.
Also since you've got a great amount of attackspeed already i'd go for wit's end as last item.

Allied

Champions that I think is a good choice to lane with is:
Amumu
Alistar
Blitzcrank
Darius (Kayle will need alot of farm though)
Nautilus
Rammus
Sejuani
Taric
Trundle
Volibear
I don't see much sense in laning with an AD or AP carry. Or someone who will need farm at all.

Opponents

Kayle has a big advantage against melee AD's and tanks, although she's slightly vulnerable to CC's such as knockup, knockback, taunt, snare and stun.
Silence and slow i guess are pretty easy to live with considering that they only last for like 5 seconds maximum.
Here's some champions i think kayle would be pretty good against:
Garen
Master Yi
Fiora
Irelia
Pantheon
Kha'zix
Gangplank
Riven
Sion
Talon
Tryndamere
Nocturne
Udyr
Warwick
Rengar
Volibear
Darius

Champions i think are the biggest threat to kayle:
Blitzcrank
Taric
Teemo
Yorick
Ahri
Cassiopeia
Morgana
Fiddlesticks
Caitlyn
Twitch
Draven
Varus
Miss fortune
Karthus
Renekton
Jax
So basically almost all ranged carrys. I included Renekton because he can get up close, hit a stunning blow, do some damage then get out of your range, so yeah he's pretty dangerous. And Jax... well it's Jax.