Back to the OP's question ("which gun"):
I've heard the phrase "car gun" from time to time, but I've never been sure of what was intended, and I agree with a prior responder who counseled that step one is to figure out what the purpose of the "car gun" is.
If the person in question wishes to acquire some measure of self defense capability but (for whatever reason) doesn't habitually carry on his person, I suppose the car gun is a substitute for the on-person carry gun, in which we're talking about handgun of moderate weight, power and shootability. And, probably, one that is more immediately reachable from behind the wheel.
On the other hand, if the person does habitually carry and handgun on his person, then the role of the "car gun" shifts to being a supplement to the carried handgun, presumably there in case the person finds himself in a situation tougher than that for which the handgun is designed -- and (as another prior responder suggested), taking advantage of the car's ability to carry more weight and size than a belt holster. For me, that "supplement" would be a stainless, pump, 12 gauge shotgun, in the trunk.
I don't employ a "car gun." I do habitually carry on my person, and on rare occasion I'll add a shotgun in the trunk, though in general if I have concluded that going to Place X poses an unusual risk of having to employ my self defense capabilities, I find a way not to go to Place X. On the other hand, I do have a "boat gun" -- yes, a stainless, pump 12 guage shotgun (a retired Winchester 1200 Police) -- which resides in a secure locker on board. The function of the shotgun is to supplement the sidearm that, by definition, will always be on board if I am.
By the way, the foregoing doesn't mean that I abandon my anti-Place X mentality once on the water. Rather, the thing you have to realize on a boat is that, unlike at home, at work, or even on the road, there is no effective 9-1-1; you are, of necessity, your own plumber, electrician, mechanic -- and security.