Felt I would weigh in on a few things. Some basic knife prep work you would do I guess. Mirepoix, fine dice, julienne, brunoise. Chicken break down, striploin breakdown, whole fish cleaning, and some line work like slicing proteins.
Mirepoix- I personally find a gyuto to be a great asset when going through large amounts of vegetable prep. I feel a vegetable cleaver will serve you just as well if not better. Basically, just because of the scoop of the cleaver. I find the cleaver excels in julienne, brunoise, but the gyuto will probably get your fine dice a little bit better, the thin profile at the tip creates less drag going both ways through your vegetables. So, your onion will stay intact better and won't get "pulled" apart by your knife sticking. The cleaver I would say is the safer knife because of it's height.
Oh ya, the santoku, no thanks in this category.
Chicken breakdown- ugh, none of the gyuto, cleaver, santoku are gonna do you much good here, get a boning knife, a honesuki or I use a hankotsu. I think if anything for a home cook a good petty will do fine, just be really careful separating bones/joints, or switch to your gyuto. Removing the breasts I do not like using a gyuto for though, chinese chefs do a great job with the vegetable cleaver. Martin Yan can clean a chicken no problem with his vegetable cleaver, but you aren't Martin Yan.
Fish- Small fish cleaning the tip of the gyuto can make due, a suji can do well with skinning after it's bones are out. But, if cleaning whole fish like salmon, a workhouse gyuto will do the job start to finish if you want, gut, bone, filet. Cleaver, nope, Santoku, hmmm I guess, but you are gonna want something longer than 200mm to skin the fish. But to breakdown and filet a santoku will do ya.