I'm metric for anything, tape measure, drill bits you name it.
Except router bits.
Don't try to fight it. Confusingly 1/4" or 1/2" are what I buy as another poster said, they tend to be easier/more common yet the actual diameters I use are all metric. In other words, my last purchase was a 1/4" shank 9mm diameter cutter - ugh!
It ****** me off, but that's the way it is.
From what I can tell it seems to be Euro countries are 8/12mm wheareas here in the UK we're stuck with 1/4 and 1/2 inch collets as the most common.
I would buy your workhorse bits in 8mm. Most of your routing will probably be covered by a few bits anyway. 8mm are not as common in stores, but easily enough to get online from Weldon, CMT (probably many others too). For small bits and one off, 1/4" will do fine. Anything that can potentially be used in a trim router I would buy in 1/4" so that you can get the trim router at some point and dont need more bits, eg rounder bits, chamfer bits.
Note that 1/4" is 6.35mm but will generally be marked as 1/4". 6mm is a different size which you dont get in the uk. They cant be mixed. 8mm bits are 8mm, they wont be given an imperial equivalent.
I use 1/4inch shank bits without problems, but I prefer 8mm. They don't vibrate so much as the 1/4" variety. It's the answer if you don't want a 1/2 router and 1/2" shank bits to duplicate all your 1/4" profiles!
Some commercial jigs are better used with 1/4 routers and cutters. (The smaller Keller jig for instance.)