The Spells I am usually using for ADC are Flash and Heal. If you don't like Heal you can go with Barrier or if you want to be more aggressive just go with Ignite.My opinion is that the best Spells for AD carry are the Flash and the Heal !

Core->These items are the most needed! You must buy them ASAP! OK! Here are the core ones:
1)Essence Reaver
2)Rapid Firecannon
3)Infinity Edge
After core items you probably need some damage, life steal and critical chance, so I would recommend one of those:
1)The Bloodthrister
2)Lord Dominik's Regarts
3)Mercurial Scimitar
4) And more that you can check at the top side of the current build.
If you are fed go for GA or Lord Dominik's Regards. At level 9 you need to change the trinket to the blue one. The enchantment for the boots may be bought at the end of the game with an elixir.

I added only 3 champs cuz I am lazy (sorry 'bout that), so here are the notes about them if you want them on 1 place:
1) Vayne: Even if Vayne is dealing good damage late game you can outplay her easily if you are not bad with Miss Fortune.
2) Tristana: Tristana. Come on why those tiny yordles are so OP??? If your support is better than their it will not be so hard. Oh late game is kinda hard against her.
3) Sivir: DANGER!!! It's Sivir she can block your abilities easily with her shield so try to wait until her shield is up before ulting or you lost probably.
This is all I can say about those 3 champs and if its someone like Varus if you know how to juke and predict his moves you will win.

I am not a professional player from LCS so probably I am not the best in the runes and masteries but you can still check mine at the top of this build. :)