The gauge has nothing to do with slinky/superslinky, that's actually related to the materials the strings are made of.
Smaller gauge (thinner) strings are more comfortable for doing INSANE bends where yiu can go easily 3 steps over the original note., BUT they sound "weak" and "thin" unless your guitar is a solid body guitar made of at least decent quality woods (not something you find in cheap guitars) and/or have HOT pickups.
Seriously, forget about small gauge strings for guitars with a floating tremolo system (like a floyd rose)
I never go under .09 they're actually comfortable and elastic enough to provide good playability and sound. But .10 is where it rocks, although they're "harder," but your fingers get used to them quickly.
Some friends use .11 and even .12, I can't play that shit, but they do have better sustain!
When I talk numbers, these are the gauges of the 1st string (thinnest). And guitar string sets are built on that. If you go to a store and ask for .09 they'll offer you different brands, just compare the gauges of the other strings and find what suits you best. Saying "the strings of my strat or LP copy" doesn't mean shit, it could be .09 or .14 sets or even fucking nylon strings or even rope.