Usually most people level Double Up first and then the other skills, I personally level up Impure Shots first and foremost, you'd be amazed how much it increases your damage output in a 1vs1 situation, not to mention people will usually underestimate the amount of stacking damage you're going to get from it with each hit (about 40 extra damage at 4 stacks with Lvl5 Impure Shots).
But yeah, I usually use Make It Rain and then fire at least 2 shots at whoever is in my lane for harassment, this will make them both towerhug and make them think twice about getting that low HP minion.
As for items, mine go:
-Survivability item (Banshee's if the enemy team is heavy on mages, or just Phage for the HP + slowing).
-Finish Infinity Edge.
-Guardian Angel if needed.
Go with what you think you'd need the most depending on your situation.