Generally if the opponent is ad I will start Cloth Armor and 5 health potions.
I personally like an early core of: boots, doran sword, and Brutalizer.
After I get the early core,... if I'm having a rough time I consider a cheap solution for added durability such as a single Giants Belt or a Hex Drinker (if the opponent is AP). Neither item will be upgraded until I get a Blood Thister and Last Whisper finished.
If you see them building nothing but health (Giants Belt > Warmog) push out a Blood Thirster as quickly as you can. If you start seeing Armor Boots and Chain Vest early, consider building a Vamp Scepter after the early core, and then buying Last Whisper before finishing your first Blood Thirster.
Also consider that the sollution to your problems is not always going to stem from items or champions. Sometimes it has to do with how well you're farming relative to your opponent. Check the difference in CS around the 10 and 20 minute mark to get a feel for how ahead or behind you are. You might feel like their defense is overwhelming, but its relative to your gold and level situation. They could have armor and health, but if you're 20 cs or a kill ahead you will cut through it like butter. Especially if you have a level advantage. This goes vice versa in your opponents case as well though.