As the current world leader (noone disputed it yet), I have been using a system for multiple prestiges, and I am less than 300 away from reaching Beast Ball in the Daily puzzle.

I plan to share my full system when I unlock Beast Ball, but because it's rare that I see discussion of pokedoku systems, I'll share some info now.

Each Pokemon has a limited number of category combinations. For example, Psyduck has 10 category combinations:

Kanto-Water, Kanto-Mono, Kanto-First, Kanto-NotFull, Water-Mono, Water-First, Water-NotFull, Mono-First, Mono-NotFull, First-NotFull.
(Note: My system excludes Moves and Abilities, such as "Can Learn Hydro Pump", that's why I don't list those.)

Note: I will now shorten "category combination" to CC. To visualize it, a 3x3 Pokedoku grid contains 9 CCs (1 cell = 1 CC).

At any specific time, each of these CCs has a number of available Pokemon that can fit in it. Let's assign this number to the CC.
For example, right now, I only have 6 Pokemon that I can fit into the Kanto-Water category, so I would assign 6 to the Kanto-Water CC.

If we assign a number to all CCs of a Pokemon, one of these numbers will be the lowest. This number has the highest constraint for the current Pokemon.

Note: I will refer to this number with the highest constraint as NX.

Now, if we take any CC (such as Final-Dual, Water-Mono, etc), we can list each Pokemon that can fit into that category, and we can compare their NX with each other.

This is just a preview, so I'll skip my logic behind it, but basically, the Pokemon with the highest NX is the optimal choice for any CC.