I think Centerfire should have been specified. Everyone should have a 22 as well as a centerfire handgun. You need a 22 for cheap practice and plinking.
For an all round centerfire the best choice would be a 38 Special/357 Magnum Revolver for what I do. The 2 best choices would be a 3" 686 S&W or a 3" GP100 Ruger.
My reasoning for this choice:
A 3" medium frame revolver like a 686 or GP100 is at the upper end of practical concealed carry size.
In 357 Magnum you can shoot 38 Special ammo, as well as Full Power 357 Magnum.
With a 357 revolver you do not loose your shell cases, good for reloading.
A 357 revolver will shoot 38 Special shot shells for snakes.
A 357 revolver will shoot factory ammo from 148 wad cutter 38 Special to Full House 357 Magnum.
A 38/357 revolver is pretty much plug and play. Any adult in the family can operate it without issues provided the ammunition is in a power range they can tolerate.
I can reload 38 Special for around $0.15 a round buying cast or plated bullets. If I cast my own bullets we are talking about half that amount with bullet lube, etc. Very cheap to feed, and 38 Special cases last a very long time.
With a Lobo Enhanced Pancake holster for concealed and general carry, and a thumb break for woods carry retention, I am good to go. I conceal carry my extra ammo in Tuff Products Quick Strips most of the time. I use Safariland Comp III speed loaders for match reloads. For town carry I will have Speer 135 grain 357 Mag Short Barrel ammo loaded and with me for reloads. For Summer woods carry I will have a couple home rolled shot shells up front followed with 4 solid reloads of some sort. Normally some of my 158 round nose match ammo for general use. I will have a couple quick strips with a combination of shot shells and solids for topping off in the field.
Your mileage my vary, but for where I live, and what I do a 3" barrel 38/357 magnum revolver would be my best choice to cover all the bases well.
Bob