Ah, the age old string conundrum.
Short answer: The best string is the string you like most, but for starters Kitty is a good choice.
What type/brand of string is best for a specific type of play?
There’s no string that’s best for a specific type of play. They’ll all have attributes that will either work for you or be the bane of your yoyoing life. That said, stiffer/thicker strings in general will handle slack and whip tricks better since they hold their shape more beautifully (imagine waving a cotton thread in a circle vs. a rope - the rope is gonna form a more distinct shape). Strings that are popular for this are Toxic strings, Kitty (normal/fat/nylon), YoYoStringLab (Type X/Ammo). Notice how many I’ve listed. To each his own! For starters though, I’d recommend Kitty because they’re way cheap but good to use. Grab a 10-pack or several in various thicknesses/materials and see what you like. As you get better, go ahead and spend on the more premium strings.
What colors of string look good with colors of the yoyo? Do you guys like to match the colors even if there are ore than one, or do you like to contrast the string color with yoyo color?
PREFERENCE. Whatever matches or contrasts with your yoyo nicely will be string that looks good. Yellow neon string is a popular choice because a)it matches well with a wide range of yoyo colours and b)it’s reallly visible, which makes it good for competitions or just so you can see where you’re landing your yoyo. Personally, I use yellow on my dark aqua/gold splash Shutter, but prefer hot pink on my other yoyos (which are black) because I find it prettier to look at.
Thickness will most directly affect response - the thicker the string, the better it’ll grab your response pads. In addition, thicker string tends to be more gentle on the fingers. Quite a few of us here prefer fatter string, but plenty of us use regular thickness too. Again, preference! Get some Kitty normal and Kitty fat, see what works best for you.
*Final point: Kitty doesn’t hold colour as well as, say, YYSL strings which are known for keeping their brilliant colour. I wouldn’t be too bothered by that at a beginner’s stage because it really isn’t a huge thing. As you play more and experiment with the various string brands and types, you’ll develop your own personal preference.
p.s. The brands I listed are not exhaustive, they’re just the main few that come to mind.
Hope that helps!