Any tips before its first range session? Does it need any buffing usually? I bought it for my running gun. Been chased by dogs while running, and this tiny gun fills the roll of my gym gun. European FMJ I read what I should feed it

Cleanliness of chamber is important to proper function.   Rarely make it past 50 rds between cleaning.

I too recently bought a P32. I did not do any fluff-and-buff. Just cleaned it and took it to the range. I've shot 150-200 rounds through it with no malfunctions. Mix of Fiocchi and PMC.

I polish ramp of all my keltecs and give a damn good cleaning.

I run Hornady Critical Defense.

Keep a 7rd in gun and a 7 rd backup in my belly band while working out etc.

I’ve had a P-32 since they first came out and I was on a six month waiting list. I’ve put thousands of trouble free rounds through the little gun. It’s so thin and so light, it leaves no excuse for not carrying a back up. It’s my BUG when I can’t carry a Glock 43.

There is a new heavier main spring, rated for the Buffalo Bore + P .32.

Took it to the range yesterday. Ran 200 rounds through her. Such a easy recoiling gun for its size. I'm a fan.  10 rd mags for added pleasure

I just cleaned & lubed mine, ran right, right out of the box for me. Have not tried any hollowpoints but no issues with Fiocchi, S&B, PPU or Magtec fmj.
I'd rather not risk rimlock with short OAL hollowpoints and KT doesn't make the spacer kit for the p32 mags anymore although it's not a hard mod to do yourself.

I first tried a Pearce mag grip extension but it's like a Pico. hangs down long enough to get your pinky on it with room to spare but really makes it harder to hide in a pocket.
With the flat factory mag plates I was only getting my middle & half my ring finger on the grip. Tried a pinky extension from a NAA Guardian and that curves down just enough to slip under my ring finger for a good solid grip when shooting one handed. And barely hangs lower than the flush mags.