The pictured shotgun is a Remington Model 11, patterned after the Browning Auto 5. Judging by the pic, the condition looks a bit rough, so value is probably something less than $200. There's one at a gun shop near me, a bit better looking than yours, and the price is $150.
Never trust anyone that's never even seen it with a question like that. If you've seen it close up and can function test, it's up to you whether you think it's ok to fire.
It may help if someone can throw in some things to look for or "gotcha's" for an old gun. I've got 3-4 like that. I don't plan on shooting them so I'm not worried. 1 of them I shot as a kid but I have no desire to shoot it now. Hell, one of them was my Grandfathers old 12 gauge that has a bulge in the barrel right at the end where a dirt dauber moved in and he didn't know it until he shot it. He used it to shoot crows out of his pecan trees back in the day.
Mainly what gauges it was offered in, how much a replacement stock and fore end are. When I got mine there was a 12Ga shell stuck in the tube, I'm thinking it might be some thing other than a 12 GA. There is no gauge stamped anywhere. The fore end on mine has a very bad crack in it, and up until now I thought trying to fix it was a lost cause. But now I feel hope may be restored.