Trigger free play acceptable or ?

[RJW NZ]

We just had a thread, that I now can't see, where the poster was asking if he needed a new trigger because his No1Mk3' trigger was very loose on its pivot.
As a result I got digging in my box of bits and matching up a number of new triggers and new pivot pins, and what I found is that most of them are quite sloppy in the pivot, and only a few have a decently close fit. None are what I'd call an well engineered fit.
I do have the correct pin/s. They're the one that are quite a bit shorter than the others, cos the others will foul the woodwork and stop assembly of trigger guard to fore end. They are mostly Lithgow parts, pins and triggers, new unused.
My question is, is there a preference either way? I can see that a loose fit on the pin would allow the trigger to float somewhat and allow the trigger bumps to land squarely on the sear when the pressure comes on from a trigger pull.
On the other hand, when handling the rifle, the less sloppy trigger feels just basically better under the finger, and the loose one feels sloppy.
Is there a preferable best, remembering I'm shooting for better accuracy, not combat?

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[Son]

Personal preference and opinion only... I'd prefer the trigger loose on the pin (it would very quickly wear to be loose after using it anyway) But if firm it would add feel to the first pull, possibly making the break at the second stage less noticeable. No, I like a two stage trigger with well defined "stop point" between the two.