I saw one recently at a gun show, they can range in price from 300 to 500 dollars.
50-100 USD
Which model in what condition?
Depending on the model and condition 50-5000 USD.
Depends a lot on which one and original condition, condition, and condition!
Value depends on Make, Model, and condition. It may range from $10-$1000, and will truly need a hands on appraisal.
.32 short used to be available from Navy Arms or try some of the local gunshows for the Navy Arms .32 short rimfire.
First remove the forearm to see if there is a model number there, it could be a 44 or 44 1/2 the latter is more desirable.
Remington didn't make a Model 1 shotgun, if it's a #1 Rolling block it could be shot out but it's no a shotgun. I doubt however you could have identified a Model 1 Rolling Block vs all the models but not know it's not a rifle. Best determine what you have and need a VERY good description (for identification) and value.
Essex was a "store brand" gun made for Belknap Hardware by at least 3 companies, most commonly Crescent. In very good condition would be worth about $125. There is no special collector's values to these, just a nice older .22 rifle.
Value of ANY firearm is based on exact make, model and condition. You have given us the make. You will need to visit and gun dealer or a gun show in your area for a hands on appraisal.
200-275 USD
Requires professional appraisal.