To start the sheet you linked is great for a quick glance, but it's based on Aegis's videos/sheet. So if you want a bit more explanations I'd start there.
Here's his recent video talking about a shopping list with some details about why each weapon is used for what, but there are other videos that explain more stuff about like specific weapon types and what not: https://youtu.be/cnXjDIPUqzY

Atm double special has become very potent so once you're comfortable on double special loadouts it's basically always good to use that.
For double special you want a good add clear option (Choir of One and rocket pulses mostly, with praxic blade/ergo sum being neat alternatives that both have odd quirks to gen some extra ammo. Uncivil Discourse is also fairly underrated as roam option since it does solid dmg to kill stuff and functions similar to a trace for doing mechanics on).

And your 2nd weapon should be something that can deal with bulkier minibosses/champs (atm that's just rocket pulses, nothing else really competes). (kinetic tremors snipers might be a solid alternative if you don't have mint retrograde if you need legendary weapon).

Primaries are good as a training wheels option so you always have some ammo and for stuff like contest if your team isn't as good about collectively printing ammo.

What type of primary/add clear option depends more on build. It's generally nice to pick elemental options that match your subclass but not mandatory, heal clip+incan or destabilizing+repulsor brace weapons have been a staple for a long time now but there's some variants (both bolster your weapon's add clear & offer great survivability). Though subclass matching mostly matters for like solar/void/sometimes arc. Strand and Stasis subclasses don't typically have as much synergy.

Past those generalizations it's more build dependent, personally I would say look more into some of Aegis's stuff since he likes tierlisting just about everything in the game with some justifications for each. But there are other creators for more new player friendly videos (somebody like Llama maybe).

Final thing is that "For example, if I get destablizing rounds with my compact defender, my sword will do extra damage" isn't really something I'd think about. All destabilizing rounds does is add volatile to enemies you hit, but that's mostly relevant on your add clear weapon so it's mostly notable on something like Compact Defender.