You don't need a casus belli in Stellaris. You can just go and say "I want that" and declare war. War Goals are what you want out of the war - the higher it is, the more you want with a max of 100 (or 99? never got that exact). You can "ask" for them to cede planets, for them to cleanse a planet (this is the same as purging) or to liberate a planet, which makes the liberated planet(s) a new empire with your ethos. Then if you're the friend making type, you can vassalize them or invite them into your federation or something. I just burn them. Then there's the other stuff, humiliation, open borders, ban on AI etc. There's only offensive war and defensive war and you get benefits or disadvantages based on your government type / ethics.
It would be easy to say that the combat boils down to whatever fleet number is bigger wins, but there's a bit more to it. Fleet composition plays a big part - battleships are great at nuking cruisers and other battleships but can't hit corvettes for example. Then there are the different weapon systems. Missiles are awful, torpedoes are very situational until you get energy torpedoes, lasers are kinda bad, kinetics are great, plasma is great. XL weapons are kinda bad. Point defences are only useful against missile and carrier empires.
And try to fight on your terms. Early game, space stations are a big hurdle to go through. Later, you can build FTL snares to drop the enemy fleet in the middle of your close range pack - which murders long range fleets. Or go full hog and build defence stations with offensive and/or defensive auras. You'll have a much better fighting chance if your enemy's firing rate is cut in half while your shield regen is boosted.