That seems like such a straight-forward, easy question to answer, and it’s not.
> personal protection at home< First thought comes to mind is a 12 gauge shotgun. I like the Remington 870 pump, but there are many good ones out there, in all types of actions. For defense, though, you need to stay with a repeater, and away from slow repeaters. That means no single shots (the cheapest kind), no bolt actions, and, unless you’ve practiced a lot and are awful dang quick, no double barrels. That leaves pumps and autos.
But then, what exactly are you “protecting” from? Burglar at night? Shotgun’s fine. Mutant Zombie Bikers, when society breaks down? Still fine. Guy that walks up to rob you while you are working in the yard? That shotgun safely in the house don’t help much, there. If you have a large enough yard that it won’t freak the neighbors, a nice holster-pistol comes in handy, here. Police/military caliber. 9mm on the little end, up to 44 or 45 on the top. Pistol or revolver is your choice – whatever your hand likes better. I’d have a 4 to 5 inch N frame in 357, 41, 44 special or 45 ACP. But, if open carry is not common where you live, and your yard is as small as mine is, that’s not feasible.
Which brings us to > concealed carry for personal protection away from home<. Not just away from the home. If I’ve got my pants on, I’m wearing a gun. ‘Cause you never know when you’ll need one. As to which one – that depends, to a large extent, on you. Are you a guy or a girl? Girls have a shorter torso, proportionately, than guys do. That means the ribs are nearer the waist, which will make it harder to conceal a holstered pistol. Especially a large one. Are you the size of Twiggy, or closer to Andre the Giant? Do you dress in as little as the law allows, or wear baggy clothes to hide your table muscle? All of this has a bearing onto what gun you can carry. I’ve always got a 642 in my pocket. That’s a concealed hammer, 5-shot, J frame 38 special. Winter or summer it’s there. When I’m wearing a coat I often have another, larger gun, but I still have that 38.
> something to shoot "varmits" that invade the yard and would either destroy your vegetable garden or that might injure pets< This is a multiple choice. Depends on your garden (where it is, how big it is) and what type varmints. A scoped 22 rimfire bolt action will work fine with rabbits or squirrels or chipmunks that are eating your English peas or lettuce. That would be a little small, though, if it’s deer in your corn. Way small if it’s hogs in your cabbages. If it’s 20x30 feet, in the back yard, that scoped 22, or maybe even an air rifle, will probably be fine. If it’s a half-acre out by the woods, you’ll probably need something bigger. And if you have a coyote after your Pomeranian, that scoped 22 bolt would certainly not be my first choice.
> and target shooting for fun< 22 rifle be real nice for this.
So, as a minimum, I’d have a 12 gauge pump or autoloader, with an 18 to 20 inch smoothbore barrel and a bead front sight. That would be legal for hunting anywhere in this country. With birdshot you could do fine with quail and or pheasants, and rabbits and squirrels. With that barrel it would be pretty useless for duck or goose, but they sell extra barrels. With buckshot or slugs you are good for both hunting deer and shooting men out to about 50 yards. Maybe even 75.
I’d have a bolt action 22 Long Rifle with a scope – either a fixed 4 power, or a variable 3 to 9.
I would have the largest caliber pistol that I could effectively conceal, no matter how I was dressed. For me, that’s that J-frame 38.
I would add, when I could, a large caliber holster-pistol, and a scoped rifle-caliber rifle. I specify “rifle-caliber” because there are many rifles chambered in “pistol calibers” - 9mm, 357, 44 magnum. While I own, and enjoy, several of these, if I was only going to have ONE rifle, it would be 308 or a 30/06. Something I could reach out 400 yards or more, if I needed to. This would be to extend the range I could shoot the deer or Mutant Zombie Bikers past the 75 yards that I could do with the 12 gauge.
That’s the five that you topped out at, but I would also get a 22 pistol. Just because they are so dang handy, and also so dang much fun.
Lastly >Would you try to get all these guns in the same caliber, or would you look at different calibers for different needs?< Most definitely different calibers for different needs.