For an occlusal composite you could just remove the area with caries and not open the rest of the grooves. Make sure the depth is good and the area is open enough to instrument the composite. Remember you have mechanical retention with composite. You could also do slot preps for class IIs without the occlusal segment.
For scaling I generally use a sickle scaler on anterior teeth and a 13/14 scaler on the posteriors. There's a 2R/2L for the anterior and 4R/4L for posteriors but the 13/14 is universal so I tend to stick with that. You are right that the 11/12 is to detect calculus.
Here you go:
Anterior sickles are mainly for superficial deposits on anterior teeth. You can go a little subgingival on a prophy but if you have deep pockets (3mm or more) on the anteriors you should use a gracey 1/2. Or a Gracey 13/14 if you know how to use it in the non-traditional way. (remember that graceys are NOT universals so use the correct side of the instrument)
Usually when we say "13/14" we are referring to a Gracey 13/14 which is specific to distal surfaces of posterior teeth. If you use this for posteriors then you should also be using a Gracey 11/12 which is for mesial surfaces. There is a universal called Columbia 13/14 which I use frequently but don't confuse this with a gracey - they are VERY different.
My prophy set-up looks like this:
Sickle
Columbia 13/14
4R/4L (also a universal but with less bend and a longer shank)
Gracey 13/14
Gracey 11/12
But I could do most prophies with just a universal and a sickle
My perio set-up looks like this:
Sickle
Gracey 1/2 (anteriors)
Gracey 11/12
Gracey 13/14
Gracey 15/16 (same as 11/12 but with more bend in the shank)
Gracey 17/18 (same as 13/14 but with more bend in the shank)
Mesial/Distal perio file
Buccal/Lingual perio file
Gracey 7/8 (good for cuspids, premolars)
4R/4L
Columbia 13/14
There are many more hygiene instruments besides what I've listed here but your school should have all of these basics. Just be careful with Graceys! There is a working edge and a non-working edge. Don't even worry about which Gracey goes with which surface just be able to figure out which is the working edge, orient it to the tooth, and go. You'll quickly figure out that it's virtually impossible to use a 13/14 on the mesial surfaces of molars.