Most important are the slider pins.
Take the brakes apart, rotate your calipers up and remove them, clean the old grease and dirt off the pins and boots then cake them full of grease. (If the boots are full of grease, there's no room for water or dirt... Don't get any grease on the rotors or pads.. But put grease on the back of the pads.)
Take a peek under your piston boots while you're greasing your brakes.... If they're all rusty underneath, there's a good chance they won't push back in (or back off with the adjuster screw) when it comes time to replace your pads.
i bought some caliper grease that would always dry up. i dont remember the brand but it came in a bottle with a brush and the one you posted does not look familiar. got pretty frustrated with having to do it twice a year. did some research and picked up some of this lube and it's been great since. on two of my cars, it's been a year+ since re-lubing so its already holding up better than what i used before. on my third car, i had to do it again but that was because one of my caliper pin boots were torn.
