While BD isn’t overly complicated once you get the hang of things, it can be a bit overwhelming to try to teach someone all of the little nuances here on the forum. But hey, i’m already known for making huge walls of text, so imma try anyways.
So, firstly, i wouldn’t say what you did in the above scenario was wrong, but with any action, expect a reaction. From the looks of that BR (battle report) you are still very early in the era since I see primarily damage units. And if that is the case, I would expect that the 1 person with tanks is a heavy booster. If that’s the case, it is likely not a good idea to start off fighting against him as he’ll have the clear advantage early game with higher resources. Later in the era, you’ll be able to even out the playing field by using better strategy (which, technically could also work early era, just hard to deal with boosters early as they can practically replace their entire army of the same size right after killing them).
So now about units. As you can see, there’s 3 different types to pick from and out of those 3, there’s an additional 3 chassis types as well as 3 ranges. The 3 types of units are Infantry (Inf), Vehicles (Veh), and Mech. Obviously the higher you go, the stronger they get. But you also likely noticed, cost differs. Most will tell you to stick with only 1 unit type to build for your army. It should also preferably match with the rest of your team if you have one. I’ll go more into that a bit later though. The 3 chassis types are concussive (conc), beam, and explosive (expl). Conc is good against infantry, beam is good against vehicle, expl is good against mechs. Now, the thing is, you usually want a fairly evenly spread chassis mix through your army so that you aren’t weak against anything in particular. Why? Because each chassis is significantly weaker when not fighting it’s main target.
Conc does 100% dmg to infantry, 50% dmg to veh, and 25% dmg to mechs.
Beam does 100% dmg to veh, 50% dmg to mechs, and 25% dmg to inf.
Expl does 100% dmg to mechs, 50% dmg to inf, and 25% dmg to veh.
Now this is why folks will tell you to build 1 unit type for your army. Because if you mix and match, you are presenting more units to take on the full brunt of the attacks from their main target. Meaning if you have inf, veh and mechs in your army and your opponent has all 3 anti chassis types, ALL of your army is getting hit by 100% dmg. Whereas if you only have inf, then the other 2 anti chassis will be working at 50% and 25% dmg against your infantry. But of course, as you think about this, it also means you are more susceptible to a focused anti chassis army. So if you have a pure infantry army and an opponent decides they want to focus on killing you, they may build a purely conc army to fight you (likely using whatever the lowest anti chassis you have as their unit type). The perk is, of course, their army is extraordinarily powerful against yours. They’ll do max dmg to you, meaning taking a battle will hurt you more, even if you win. But of course, this also means if someone comes in with a tank army against them, they stand practically no chance. So if you had a significantly larger army, but it was mainly conc vs a tank army, you’d likely lose. Even with 3x as much army (of course, depending on their chassis build). The other thing to take into consideration is that there are some unit advantages. Inf have a bonus against veh (so beam inf are strongest counter to a veh army, and veh have a bonus against tanks (expl veh are best against mech armies). Mechs have no bonus, but they are already so powerful, they really don’t need it against inf.
Still with me? If so, cool. (Im so sorry). If you haven’t made it this far 
i’ll keep going anyways.
Now, there’s yet another 3 way factor to take into consideration here (just for setting up your army). This is armor, damage, and range. These are pretty self explanatory, but just incase, i’ll go over the basics. Armor has a range of 1, but high hp. It soaks up the damage from enemies and will ALWAYS be the 1st unit to be hit within that unit type. Essentially, protecting your dmg and range units of the same type (meaning armor tanks won’t protect range infantry. Only other tanks). Damage does more damage to enemies obviously, has decent hp and a range of 2. Range has a range of 3, low hp, and decent dmg. Longest range hits first. This means armor units won’t even attack until round 3 of a fight (and usually, battles are over by round 3). I highly suggest you play with the battle simulator when you get the chance to see how things will play out. Just have fun with it and test some theories out on builds. It’s a great tool.
NOW, we get to the crazy complicated part. What is the best build? This has been a question many have pondered (and many think they have the answer to). Now, as you continue playing, you’ll likely run into the term “Pro Build”. This build is 30% armor and 70% range (for any unit type). Now, quite honestly, this is a very solid build for an army. But, it was made with perfection in mind. This army type is best for maximizing damage when you are at an overwhelming advantage. Whether it is with a nuke, a spy, or just simply bigger numbers. This build was made with the mindset that you would NEVER have your 70% range ever get hit. Only the 30% armor should ever be lost in a battle. This is of course a hard feat. And honestly, MOST battles that end wars are much closer in number between army sizes. With this being the case, damage units are actually more powerful, assuming you have the armor to soak up the damage until they can start firing away. But a build like that would require extremely high activity so they never get hit by a nuke or spy (which would absolutely cripple it). It’s also a costly army to replenish as it will assume high losses. But also a cheaper army to originally build than the “pro build”. But, you’ll find a majority of players here stick with the pro build. With that in mind, I would highly suggest you play with the battle sim and see what works best against it 
Now, i haven’t even gotten into using spies or nukes yet, and I think i’ll pass on doing so here. If I keep going on, i’ll probably end up just rambling on how to play the entire game. So i’ll just say, for now, play around a bit in the battle sim.
