In Mystery Writing, work backwards from your Mystery
Please note- I'm aware that the Original Poster stated that they're not really running a mystery adventure:
The focus won't so much be in really solving the mystery like in a
detective story either, ...
...but I felt it important to answer the question as written, to benefit future readers who follow the thread. Hopefully this helps the OP as well.
In the scenario you've described, there is a correct answer- just one that can't be answered without knowing your central mystery. You need to start with the mystery your characters will need to solve, determine what clues will lead a party there, then determine the mix of skills needed to follow the clues. Once you know that, you can distill those skills to the smallest possible party with the mix of skills to get the job done.
I've been crafting a mystery adventure for eventual publication, so I have a bit of practical knowledge to share. I'll try my best to avoid opinion and lean on examples.
a) What is the Mystery?
As alluded to in this link, everything in mystery writing hinges on the central mystery that needs to be solved. Two key bullet points from that source:
- Know the ending of the book in advance. Then you can build toward it.
- Make a list of clues that point to the murderer, which you will
scatter throughout the book. Decide which is the crucial clue that
will solve the mystery.
b) What clues would lead a party there?
For this stage, follow the great advice of The Alexandrian and use the 3-clue rule:
For any conclusion you want the PCs to make, include at least three
This adds a ton of work, but helps ensure the clues the players misinterpret and miss won't completely derail their investigation.
c) What skills or talents would a set of characters need to solve the mystery?
Working backwards from your mystery and the clues needed to solve it, figure out which mix of character skills will be needed to reveal the clues. Since you've stated you intend to guide character creation, you can ensure the right mix of skills are present in the party to uncover the clues. Balance will be important here- you'll need to make sure every character gets a moment to shine, so try to have some clues revealed through combat, some through magic and some through stealth.
Don't be afraid to go back and revise your clues from step b if a character is getting overlooked, and try to use the 3 Clue Rule to make sure different character types could find the same clue (i.e. the fighter could get it by defeating a henchman, or the rogue could sneak into the henchman's chamber and find the same clue)
d) Distill that down to the smallest possible party.
Here is where the actual answer to your question lies. The best sized party to solve a mystery is the smallest possible group with the set of skills needed to solve the mystery