Runes

Greater Mark of Attack Damage
9
Greater Seal of Armor
9
Greater Glyph of Magic Resist
9
Greater Quintessence of Attack Speed
3

You should be taking either AD or Lethality marks. I prefer AD for the early damage (pre level 6 or so) because for Draven it's very easy to get a kill with an extra 10 or so damage every auto attack that Lethality wouldn't give. That being said, if you plan on going Youmuu's Ghostblade then Lethality marks have a place. I still would go AD, but Lethality scales with more lethality and getting 30 or so APen at level 10 is something that shouldn't be underestimated.
You take armour because it's the most stat-efficient rune you can take through seals. Flat HP seals also give good stats nowadays, but armour is just straight up a better stat to take on bot lane. Both aim to make you tankier but armor is better for that when you're laning against an ADC. People argue health vs armor, and armor is better for 2 reasons. First is they're cheaper IP wise making them more accessible and second your effective health is similar to that of pure health, but your other stats like lifesteal become more effective as you have less health to refill. The difference is really small, but there is still a difference none-the-less.
You take magic resist here because again it's the most stat-efficient rune to take. With supports dealing a lot of magic damage (usually) and Thunderlord's Decree still being fairly common having a nice barrier of MR is very helpful. It also helps when the enemy mid roams, as they always seem to do against me. You can take AS or Mana regen here as well, but I prefer the tankiness vs magic damage way more than the extra 5% attack speed or 1.3 mana every 5 seconds. Preference.
The standard AD carry page consists of 3 attack speed quints. This is because AD quints are not that efficient in comparison. 14% AS gives you a great auto attack animation allowing for better last hitting and just generally feels a lot nicer. They just feel good, and everyone uses them for a reason.

Pros / Cons

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Pros


+ Powerful Harass
+ Reletivly Easy Farming
+ Global Ultimate
+ Stupidly High Snowball Potential
+ One of the Highest Potential ADC Damage
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Cons


- Can be shut down with hard camping
- Seriously, you'll get camped
- Very Difficult to pickup
- Even harder to truly master, One of the hardest in the whole game
- No hard escapes (like Arcane Shift