Again, sizes are up to you, but since your budget restriction is an issue, maybe 3 sizes spread out from small to large to fit as many applications as is possible.
I use many different types of hooks, especially for tying flies. Some I use interchangeably if the size is available, and they have sufficient strength. The label given to the hook, makes no difference to me, it's the dimension, strength and sharpness I want, and for some the shank length and gap are important attributes.
Various brands have hooks that they label "O'Shaughnessy", but when comparing brands, you may see a physical difference in the appearance, so that name isn't necessarily a good indication of whether the hook will be well suited for the intended purpose. My idea of a true O'Shaughnessy style is Mustad 3407, or 34007, or Eagle Claw 253 or 254 type hooks. Gamakatsu does produce a similar hook, but they have others that they use that name, and it looks different, more like that SL12S.
I use straight eye Octopus hooks for the same types of applications as I use the Owner Mosquito, and various similar hooks labelled as "Live Bait" hooks. It doesn't matter the name or label, it only matters that the hook does what I need.
For plastics or live baits, hook gap and wire diameter is important. When the wire diameter is too heavy, it creates problems with the plastic or bait, and frankly the only way to determine if a hook is a good choice is give them a try. I don't use some live bait hooks for my flies, or for baits, because the wire is heavier than I need, but I still will give a pack a try sometimes. Some of them also have kirbed or offset points, which is fine for bait, but not what I want to tying a fly and most of time for a plastic.
Gamakatsu produces a wide range of hook types, and IMO, some are similar enough to be the same hook, yet they apply a different model number and name to them. It only matters to me that they do the job I need from them.
For what you need, you're the only one who can determine if the hook is correct for applications. I've added as much insight as I can, but my use and yours are not all the same. I know that's not a helpful answer, but it's truthful. Get a pack of the hooks and try them is the only way to see if they work for you.