Muzzle breaks/compensators reduce muzzle flip under recoil by redirecting gasses up or to the sides - and yes, they can make things louder. Buddy has a SCAR17 and while it weighs 2lbs less than my FAL it recoils less and has less muzzle rise. BUT you better use both ear plugs AND ear muffs 'cause it is freakin LOUD.
Flash suppressors reduce the big ball o flame that you can get with some rounds (esp. in shorter barrels) by venting gasses up/down/sides. They too can make things louder. Military ammo is usually loaded with powder designed not to create a lot of flash....
Note that not all flash suppressors can function as breaks, and not all breaks functions as flash suppressors, but combining the functionality is very common (esp. on military type rifles).
Accuracy wise - ANYTHING that changes how a barrel vibrates can affect accuracy - and it can make it better or worse. The Browning BOSS system is basically a weighted muzzle device that as you screw it in/unscrew it it changes the barrel harmonics.
Since you are living in CA I'd say skip whatever evil features you can to get removable magazines - esp. since I think that flash suppressors are banned in CA. See
https://www.calguns.net/calgunforum/showthread.php?t=1270467
FWIW I tend to shoot my FAL with the muzzle device off (it is a G1 kit, muzzle device isn't threaded it slips on and locks into place). And on my 9mm AR build I can't tell a difference in volume, muzzle flip, or accuracy with or without muzzle device (A2 style birdcage like a bog-standard AR15).