The biggest diameter you can use will help to reduce chatter, so 3/8". But also I would be looking at a carbide endmill, simply due to the increase in rigidity. North American suppliers of those will be very expensive, but an 8mm carbide will easily outperform a slightly larger 3/8" (9.5mm) HSS endmill - the carbide is 3x stiffer.
So a 8mm asian sourced endmill should be about the same cost as the KBC one after shipping, give or take $5-$10, unless you are already getting stuff from KBC or can walk there...
quick examples:
https://www.aliexpress.com/item/1005003179556695.html $37.58 shipping in
https://www.aliexpress.com/item/1005006117203437.html $37.31 ($31.99 + $5.32 shipping)
(I don't think the border people have figured out the T word on this stuff yet so there's that savings too, not that we all shouldn't pay our share, just nice to get small break once in a while.)
I rarely check the jungle store, but today they seem to have something that fits the bill even better than above - 3/8" carbide for less than the KBC HSS:
https://www.amazon.ca/Carbide-Cutting-Diameter-Stainless-Aluminum/dp/B0D12TFQL4 $30.99 minus $9.30 coupon = $21.69 seems worth giving a try. gets you full 3/8" diameter in Carbide and 1.375" flute depth. (basically 35mm).