Old Remington 870 Wingmasters are the best deal going for shotguns. You can probably find a serviceable one for around $200-$300. Most of these come with a fixed full choke and 2-3/4" chamber. Reaming out the choke to Modified will make your gun good to go with steel shot and will work as a good all around choke for the uses you specify. If you want choke tubes, you can swap out a newer Rem-choke barrel.
While conversion to 3" isn't absolutely necessary, if you want to do it, there are two things required. The first is a 3" chambered barrel and the second is a 3" ejector, which will prevent 3" shells from hanging up on the ejection port. The only downside is that the rivets will show unless you have the receiver reblued after the ejector is replaced.
It would probably be a good idea to get a dedicated slug barrel because they are shorter and have sights.
The Ithaca Model 37 is also a fine shotgun. The older ones are all 2-3/4", with only the recent ones available in 3". Once again, you will want to have a full choke opened up to modified. Guns with a serial number above 855,000 have interchangeable barrels, but I don't know if there is a source for them in Canada.