The basic device for the number of troops in your barracks is to have 5 full teams (40 troops). Fewer and you run the risk of a unlucky run of missions and not being able to man a full squad. Too many and you start to waste xp. That being you want to be investing xp into the troops you are going to be using. The most accurate answer is that it comes down to your playstyle, level of risk you take, etc... but 5 full teams seems to be the consensus. Personally I like to run with 6 full teams, and the 6th team is the pool I go to when someone becomes injured.

If you are new to LW you won't know what type of troops you need some you might want a slightly larger barracks so you can experiment. That's perfectly sensible.

The MEC issue, I'm not sure I can help you. It appears that Johnny L is contemplating another iteration of MECs as he homes in on the sweat spot for them. Rather than look at their weaknesses, consider there practicalities; they carry one of the largest guns in the game, some come with very good offensive perk combinations, once grenades arrive they still offer the best tanking in the game. You'll still have to use they in the late game. You might as well experiment with them now.

Finally, and connected with the previous two points, Long War is complex, and its all about synergies. "Mastery" takes a bit of experience and a lot of mistakes, don't be afraid of save scumming, and I'll go one further, make a save point, order something like a MEC, then fast forward through the game to when it arrives and give yourself the opportunity to experiment with it. Things on paper may not perform in the field as you'd expect. That Goliath may be more useful than you think.