Build barracks, marines, use those scvs to block ramp to prevent ling rush. Then scout when you have enough marines blocking. Micro marines if they're being attacked.
If you manage to find zerg expanding (made hatchery his 1st building) and managed to contain him with marines and scvs only. Tech to tanks and be really aggressive but don't let tanks die.
(Once I contained a zerg, but eventually lost because of cliff lurkers, mutas were sent to my base (much later on) and most importantly, I wasn't aggressive enough). Just use your tanks to destroy whatever building.
If you want to cripple his economy early on (say you dropped onto his base and there's no defense but you know you'll die soon), go for the gas first(imho) because gas is crucial for mutas and lurkers. Enoughs M&Ms, and tanks will own zerg unless they get these units.
Tech to M&Ms, when sending to his base, don't make them go in a line because lings will own them. M&Ms can take maybe up to 3 sunkens unless zerg has reinforcements(probable). Get out if there are lurkers. But try to kill one at a time if they come after you.
Upgrade marines from two bays, early on. (imho) Upgrades can really make a difference, especially with stimmed marines.
Get one wraith, kill overlord near your expansion. Go overlord hunting, DO NOT LET IT DIE. Use it later on for scouting and further hunting. Sometimes if the zerg doesn't even have a den, you can own him badly. (Once, I played someone random, teched to factories quickly like a TvP, found out it was zerg, got one wraith and basically made him leave the game angry.)
Tech to science vessels, early on, upgrade irradicate, AND the extra energy later on(imho). The extra energy gives them three irradicates instead of two (shrinks number of vessels, saving gas), and gives vessels around 60 or 70 energy when they come out instead of 50.
Build one bunker + 1 turret at the backside of your mineral line, sometimes you can even fill it with like 1 or 2 marines. This usually scares off mutalisks. BTW, mutas with defense upgrades will own M&Ms (depending on number).
Get tanks/bunker/turret out of your expo. You should make natural expansion.
Use irradicate to counter guardians, kill their drones, etc. Harrass him. Irradicate lone lurkers, ultras, etc.
Kill his expansions, but scan first (I once didn't and died from guardians in his expo TT).
Use M&Ms, tanks, and vessels (with scvs) to attack his bases.
Do not go for BCs, unless zerg hasn't teched very much, or doesn't have many hydras.
*Starcraft, unlike Warcraft III, is mostly an economy game. If you destroy his expansions, and defend off his forces, he cannot win. That's one way to look at the game. So instead of focusing on destroying his base, focus on not letting him expand. Then kill him.*
I don't consider myself a gosu so any "constructive" and "helpful" criticisms are welcome. And you don't have to PM me.