Macro, Composition and Positioning

I watched the entire replay and I saw three things I would have made differently. 

1. The most important thing in SC is macro. With macro alone, you can win most games and get in the higher leagues, until that point, you don't have to worry about fancy micro but really focus on bolstering your macro. For instance, you were floating 2k at the 10 minutes mark and in the late game you had 5k but 130 supply. You want to have a plan and think ahead to keep your money down. If you see you're getting more money than you can spend, throw down a couple more rax, another engi bay or a second starport. You want to be able to build fast because minerals don't shoot but marines do. Before you get into the game, have an idea of what you want to do. Your first push was the kind of thing I used to do when I didn't know how to win and was just hoping that my opponent was as lost as I was ;). 
2. Second point is the composition. Marines tanks use to work very well in WoL in TvZ but not so well in HoTS. Zerg can know use the swarm host to contain you or the viper to negate the effect of your tanks in big engagement, plus the counters they use to have. Pure marines can't stand against ground zerg so I'd suggest you try some kind of MMMM, it's been working quite well for me, I have an 82% win ratio against Zerg. The sample is quite small but promising.
3. Lastly, your positioning favored containment. By setting yourself on the high ground and holding from there, you made it easier for the zerg to contain you. I would have set myself down the ramp, maybe throw a couple rax/bunker/depot to help manage the flow of units, and expanded in the above slot with a PF. It gives you more mobility and allow you to spread your units which every Terran playing bio wants to do. Zerg are scared to death of mines. Put some around your expansion and they'll think twice about sending a couple lings to ruin your day. 
Good Luck and don't despair, we've all been through that!