I live and hunt in Wisconsin, where we have a very strong deer hunting tradition. Originally, deer hunting zones were designated as shotgun only (usually near urban areas) and rifle and shotgun zones. Not to many years ago, pistols were also approved for deer hunting. I also hunt with a blackpowder muzzleloader (we have a special season for those). Now, rifles, pistols and muzzleloaders are allowed anywhere. I originally started out with a Remington 870 pump 12 gauge, with a smoothbore "slug barrel. Shooting 1 oz. lead "pumpkins" (slugs) was pretty ineffective over open ground; better in brush. I bought a rifled slug barrel and that made a great difference with sabot slugs. About that time the rules changed and I haven't used the shotgun on deer since.
I switched to a Remington 700 bolt action in 30-06. and had great success for years. I picked the caliber because it is common and easy to reload. It will drop anything found in our State. I put a high end scope on it. A .270 caliber will shoot flatter, but I have my 700 sighted in and I'm comfortable with it. I have a number of pistols, both revolver and semi-auto. I was lucky and most of my purchases were made off the record from private individuals. For small game you can't beat the Ruger 10/22.
If handgun restrictions coming your way are an issue, by all means purchase one first, hopefully from a reputable individual. Think carefully about what you will use that handgun for and buy appropriately. Just as in buying "a" boat, there is no one firearm that will do it all. Prioritize your purchases based on use and anticipated future restrictions.