I don't know what a "Fighting" shotgun is but if that means "Tactical" or "Combat" then it should have a short barrel (<20") a large capacity magazine (tube or box fed) a stout stock and ultimately be reliable in all weather. And by weather I'd ask (myself) is this going sweat and freeze on a regular basis - Nickle, Parkerized or a Nitride finish. I would stay away from Blued metal for a trunk gun.
The next question I'd ask (myself) is how many bad guys or bears I'd think I have to take on in one engagement. Two or more I'd want a semi-auto. One at a time a pump does just fine. A pump will do just fine in practiced hands on multiple threats but there is always the chance to short stroke it. A good top quality semi will eat all your ammo under duress in a matter of seconds.
Lots of pumps will fill that bill on your budget with money left over. A few semi-autos will come in under or just at.
I have three - Bennelli Super 90 (just love this gun, a little ammo specific) a Mossberg 500 (trust my life to it,) and new to me haven't shot it yet
but everything I've heard - it's the "Best" tactical shotgun ever made - Remington Versa-Max. (Is not finicky about ammo, quick to point, comes ready out of the box for a top tier 3-Gun Match. (Also the most expensive of the three)
I personally would not leave a Versa-Max unattended in a locked vehicle for long. The Mossberg - no problem - stolen - oh well.
Good luck with you hunt. I think an 870 or 500(590) would suit your purposes just fine.