You got a real steal.
Since you don't know how many rounds have been through it, I recommend ordering a new factory weight recoil spring from Kahr.
Don't install any extra-power springs, that almost always makes trouble. These are designed to use a very specific spring weight.
They seem to love running with a little grease on the frame and slide rails and the outside of the barrel and recoil spring.
No work on the trigger is needed, it's perfect as-is. If you've shot a DA revolver much, there's not much transition to the Kahr. It was designed to feel like a S&W revolver trigger.
Pay attention to the info on the 200 round break in period, and pay strict attention to the details of loading from slide lock-back.
These tiny guns have strong springs and not a lot of slide to grip, so people routinely try to "sling shot" the slide to load and it jams.
They invariably blame the gun.
This is simply a different manual of arms for the Kahr pistols.
These are almost always 100% reliable guns and if you have problems, either shoot it more, or try a different brand/type of ammo.
One Kahr quirk.... magazines tend to shed rounds if carried in a pocket or in some magazine carriers.
Shop around for a magazine carrier on the Kahr site, or look for one of the plastic single mag pocket cases or one of the slip-on plastic covers.