There are too many ways to laugh to just stuff them all in the general packaging of "so-and-so laughed" giggle snicker snort guffaw howl smirk ... they're not just synonyms for spicing up your text. Each one has a look, a sound, an emotional context.
I'm prone to an evil-giggle when laughing out loud personality. Otherwise my eyes just dance with silent laughter. My Best Friend will snort and smirk, or give a half smile that is almost all in his eyes. My mom giggles and simpers. My dad laughs silently while slapping or pounding his knee.
I think this is a great question because it's these little details that are so easy to gloss over, yet could provide so much in the way of world/character building.
How a person laughs, expresses (or suppresses) joy / mirth / entertainment tells (I should say "shows") much about that person. My Best Friend and I are both introverted and nether very demonstrative with our inner most emotions. The more we enjoy something the quieter we enjoy it. We might laugh politely at something that is remotely funny in a social setting, but only guffaw if caught off guard while under other unrelated pressures.