If all you care about is tournaments and not world map combat, then you want to skip them. Currently the only reason to do the optional squad size techs is for an easier world map or more free troops from wonders/events. You will likely save more troops with skipping the tech than what you would get by the free increase.
A word of caution: do not be surprised if in the future a change to the game makes this comment obsolete, with most people skipping all the techs it is possible something may change in the future.
Once you have access to all troop types (around chapter 3) combat is pretty much the same strategy. It gets more complex if you start to use non-barracks troops, then your chapter and race start to become important in such a discussion. As you mentioned you are new to combat I would stick to the basics for now and work with barracks troops as a default. Some obvious places to deviate from barracks are tournaments where cerberus are key or if you are an elve then the blossom mage can also be useful.
These threads can start you out very simply and work up your skill set from there.
https://us.forum.elvenar.com/index.php?threads/combat-101.4968/
https://us.forum.elvenar.com/index.php?threads/combat-201.15034/
Using the gems of knowledge website your troops would put you in the advanced group, but if their tactics are also advanced it might be too much to take in initially.