(Ok, sorry that I had to use 3 posts to fit everything in, was only allowed a 5k character limit)
Looking around, I see so much "TvZ is IMBA towards Z" - why? I'm having no trouble against zerg, I haven't had a zerg take a game off of me (barring absolutely stupid stuff, like an all in baneling bust that I scouted too late, so getting epically cheesed out) in a very long time.
So. A few things:
Zerg almost always FE's. If I can't apply some sort of bunker pressure early, I'll try to disrupt this with an engineering bay, something to delay it, or get really fast banshee's out. He's not attacking anytime soon, I can even grab my expansion relatively quickly, with 1-2 bunkers. I'm not sure how this works at the lower levels, but for the most part, pre-diamond is an exercise in improving mechanics and scouting/countering cheese. I got to Diamond simply by working on my mechanics over and over again.
Ok, so, you've either put a bit of pressure on zerg early, taken your own expansion (leaving you happy- if you're on an even number of bases as zerg, you can relax a little bit, pressure's now on them), you've forced him to build something besides workers, great. Now comes the oh so scary and annoying Mutalisks. (What zerg doesn't go muta? I'll cover that later). You know this. I personally throw down an engineering bay, and place a single missile turret in each mineral line. Those are safe mineral lines. It takes awhile for him to get the critical mass of mutalisks needed to do real damage.
Seeing the muta's come out, I continue marine production, and start thor production. If those mutas do try to snipe something, they'll take terrible, terrible damage from the thor. It has a whooping range of 10- I'll park on in the middle of my base, and most of the time mutalisks never darken my sky after.
While all this fun stuff's going on, I try to apply pressure. The moment I stop applying pressure's the moment I get in trouble. After the muta's are mostly gone, I start thinking about taking my 3rd. It's completely map dependent, but I like my 3rd to be between my main/natural and his main/nat. I'll move my entire army* to there, set my rally points there, and make the curse of every non-terran: The planetary fortress. So much "OMG PF'S ARE IMBA!" rants going around, well, since everyone has such a hard time with them, let's make them. A missile turret or two in the mineral line, and viola. Happiness. Please oh please zerg, attack my 3rd. (If they do, be happy. Get those SCV's repairing everything.)
*Leaving basic defenses behind. A thor at the main, a bunker full of marines at the natural, little things to stop/slowdown runbys
So, we're getting to the late game. I've been making thors and banshees, because I like them. I use hellions and marines as a mineral dump (since thors are banshees are so gas heavy), work on my upgrades (GET THAT ARMOUR.), and see if I can snipe any greedy zerg expansions. (IE they're too far away from his main). Since my 3rd's between my natural and his base, (Or somewhere sneaky and easy to defend, like an island), I'll generally intercept his army if he trys to simply bypass me and go and kill me. (Or crush it between my base and his army) Constant little pokes, see where damage can be done. Control that creep, it's useful. And so annoying towards zerg. Push when you feel happy.
My APM's only ~50 or so, on average- rediculously high APM is not needed to pull this off, and spamming is involved in the APM count.