I like to start Doran's Blade and one health potion on Twitch, always. After that my first back goals are, in order of priority: vamp scepter > bilgewater cutlass, stealth ward, first tier boots. Try not to back until you have at least 1475 gold. If you're forced to back before you have 800 gold, often a second Doran's is more helpful than a longsword. Always rush BORK on Twitch. Then you can alter your build based on how well you're doing - lots of gold, go for Infinity Edge, a little less, Statik Shiv or Youmuu's. Never build Triforce on Twitch.
I don't really understand your question about Kog'Maw - could you clarify a bit?
Twitch's early game is somewhat weaker than more predominant lane bullies such as Draven and Lucian. When your opponents first get to lane, check the enemy adc's items and what their attack damage is compared to yours, to get an idea of how trades will likely play out. The enemy support and your supports are often what makes the difference in who wins bot lane. Twitch prefers a poke and sustain lane with strong peel, so a support like Nami or Janna will work in your favour. He has a lot of trouble with aggressive, all-in supports such as Leona and Blitzcrank - the best advice I have for you should you get into a lane like that is to constantly move around as you farm and stay away from bushes.
Twitch's Q is his only escape, and it's not a solid one at that. You almost never want to use it aggressively pre-6/bilgewater, unless you have a clear advantage. Keep it off CD just in case you might need it. A lot of beginner Twitch players make the mistake of maxing Q first - don't do that. Start with E, max it first. Put a point in your W at level 2, but after that max Q second. If you are ahead in lane, you can get away with some very funny assassinations with the following combo: Stealth right next to your unsuspecting target, activate ult, W them, activate Bilgewater Cutlass, autoattack until your passive is fully stacked, and then E.
As for lane match-ups in Twitch's favour, other ADC's with a weak laning phase are normally his best bet. Kog'Maw, Ashe and Ezreal are some examples. Try to avoid picking Twitch into an enemy ADC that can zone you with superior range and trading pre-6. Draven, Lucian and Caitlyn are prime examples of lane bullies that he will have a hard time with.
The most important thing, as always, is practice. If you can make it to lategame, this is where you will start to have fun as teamfighting is where Twitch really shines. Before then, just focus on your farm, ward for ganks, and let your support worry about poking/initiating.
Good luck!