First, many guns, not just Kel-Tecs are fussy about ammo.
These are some of the common ammo complaints with some Kel-Tec P-3ATs:
Sellier & Bellot have hard primers and sometimes don't fire.
This has been fixed with good results by some by clipping three or four coils from the firing pin spring.
Steel cased ammo such as Wolf have had failure to extracts (FTEx).
Aluminum cased ammo such as CCI/Blazer have had FTEx's.
Winchester White Box (WWB) has had FTEx's.
The best thing to do would be to shoot about 200 rounds or so through the gun with ammo other than those mentioned.
If you keep the gun clean and lubed during the 200 rounds you should have little or no problems with ammo.
After shooting the 200 rounds and the gun is well broken-in, then you could try some of the ammo mentioned as problematic if you chose to.
Personally, after shooting about 300 rounds of Federal American Eagle FMJ, Remington Green Box FMJ, Santa Barbara FNMJ, Federal Hyra-Shok JHP, and Speer Gold Dot JHP through my P-3AT without any problems, I then shot 100 rounds of CCI/Blazer and 200 rounds of WWB with no problems. I haven't tried Wolf or S&B and don't intend to.
I have settled on WWB for range work because it's inexpensive, reliable, quite accurate and quite clean; and for carry, a combination of Santa Barbara because it's a powerful, accurate, non-expanding round and Gold Dot because it's supposedly a good expanding and pretty good penetrating round from a P-3AT.
I may change my expanding round to Cor-Bon DPX after some more people post the results of tests. So far, from all I've heard it sounds like very good stuff.