normally i open against with a banshee opening but since he was random i went for 1rax fe and although i won (because he dc) but i need some guidance especially the engagement!
I haven't watched the replay but I can give a bit of information on TvT and openings etc.
The banshee build is a solid opening as is all openings on one base (marine tank push, hellion drop) as long as you do damage otherwise you put yourself quite behind before really even getting into the match. Therefore if your a player just starting out (sorry don't know your rank) I suggest starting with a 1 rax fe and putting the pressure on your opponent to try and stop you from gaining an early economic advantage.There are also some sneaky all-ins which are cool to have up your sleeve for easy wins or in tournaments to baffle your opponents (proxy marauder,thor rush etc.) When doing the banshee opening its important that you transition into an expansion then into the standard terran structures (TvT) i.e. 3 rax with upgrades,factory, reacted starport and engineering bay for upgrades this is the basic structure for two base;you can add two more rax when you have enough minerals.You can then expand adding another factor more rax a armoury and another engineering bay for continued upgrades.Also in TvT mech is quite good but I'd suggest getting used to the standard way of playing TvT first.
Starting out its best to make sure your constantly building scvs, not getting supply capped and not sitting back in your base the whole time (testing the waters-see what kind of army your enemy has:having map control),also constantly building units.I hope I have helped mate glgl!!
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