If a few exceptions (e.g: Caitlyn and her snare), it's always smart to get your offensive/damaging spell first (usually q), then your escape/utility spell, then the last one, maxing out the offensive, "last one" then escape, and of course grabbing ult along the way.
Last Whisper/Black Cleaver/Trinity Force
If a champ is reliant on physical spells (usually if they have 2 or more physical damage spells) (e.g: Ashe, Caitlyn) you get Last Whisper, if you basic attack repetitively (e.g: Vayne, Varus), then Black Cleaver is your armor reduction item. The last choice would be Trinity Force, for if you have on hit effect spells (TF, Ezreal)...or are just Corki. Usually champs that need Trinity Force (enough speed and health) don't need a defense items, so you could/should grab a Last Whisper or Black Cleaver as well.
For champs that deal a huge burst of damage, you should get Guardian Angel, as when you come back, you have more chance of getting a kill (e.g: Draven), but most carries just get killed the second they come back (mainly because they don't have a lot of CC/escape spells/life steal), so Banshee's Veil would be a good choice, stops your from getting CC'd and having no change of running away, also helps counter the AP carry that's focusing you and gives you HP/mana.
If you're not very good at handling your mana/your champ uses a lot of mana, you could either get Chalice (e.g: MF), mana masteries (Build 2) or mana runes (Build 1).
For defense, flat armor (seals) and magic resist per level (glyphs) are perfect, of course armor/level beats flat armor by level 4, but it saves you from buying more non-jungling runes.
As for offense, physical pen.>AD, for there are only two physical penetration items and ****load of attack damage ones, so if you got really OP, and they enemy started stacking armor, you have the better bet (or when you land vs Rammus).
Ignite and flash are like the surefire spells first AD carries, so they don't feed or get ksed by the support/jungler. But some champs can't quite burst the enemy down (e.g: Ashe), or carries that play assassin-like (e.g: Vayne) so heal would be a better choice instead of ignite (refer to Build 3 masteries).
First Item/Stacking Doran's
You should either get Doran's Blade of boots + 3 health pots, if you have a support with a healing spell, Doran's Blade is a better choice as you could last hit easier and you don't need the bots. Really, you only need to stack Doran's Blade if you're losing (esp. if you started with one), you should farm until you could afford a Bloodthrister or B.F. Sword, farm 40 minions and have a more effective item than 2-3 Doran's. Another "losing item" would be zeal.