By three gun combo, I mean some sort of long rifle, a shotgun and a handgun. The basic gun collection for self defense and predator control. Where you live and what kind of firearms you want determines which guns might be best for you.
If you lived in the country, a pump shotgun by Winchester, Remington or Mossberg with a 24" barrel and a hi cap magazine, a scoped 30-30 lever action rifle by Remington, Marlin or Winchester and a 4-6" barrel .357 magnum revolver like a Ruger, a Taurus or a S&W might be a good pick for you.
In the city, or if you're in fear of urban collapse or riots or the like, you might want to consider weapons with a higher rate of fire, a higher capacity for cartridges and cheapness and availability of ammo. You might want an assault rifle with a collapsible stock like an AK-47, an M-1 or a Mini-14, a pistol grip and/or folding stock pump shotgun by the same makers as listed above with extended magazine and an 18" to 20" barrel for working close quarters. As a pistol, the Glock model 19 would be ideal, as literally boxes of shells could be carried in spare magazines in a bailout bag. You could carry this arsenal and spare ammo in a single short heavy duty duffle bag if the time came to flee the city.
First of all, you're going to have to go to gun shows, or deal with a dealer that handles quality used firearms. I tend to avoid pawn shops but sometimes deals can be had. If you're really lucky, you can make a package deal with your dealer if he goes to gun shows and tell him what you want. He might be able to wheel and deal you into some nice guns. Or he might have what you want in stock. The more adaptable you are, the better of a deal you might get.
It's very possible to find very lightly used "name brand" guns for reasonable prices. Like everything else, most gun prices drop fairly much after a few years of ownership. So my theory that you can still assemble a three gun defense arsenal for your home depends on buying mostly used guns. True, there are some very inexpensive new guns, but I prefer to go with the major names in firearms.
Here's my suggestions:
I figure that you can get a used Winchester Defender or Remington 870 or Mossberg or other pump shotgun used for in the $200 to $250 range, somtimes for as low as $150.00. I prefer a full stocked model, but there are lots of folding stock and pistol grips shotguns out there. Either 20 or 12 gauge are available, but the better defensive ammo is going to be available for the 12 gauge. I prefer #4 buckshot followed by a couple of slugs but many of my friends like 0 or 00 buckshot, again followed by a slug or two in case the shot doesn't stop your attacker.
Whatever shotgun I selected, I'd buy one of the cheap stretchy fabric stock covers with extra shell loops (if the gun has a stock) or one of the mounts that goes on the receiver that holds extra shells. I'd also get some sort of flashlight mounted to the front end of the shotgun. These are all relatively inexpensive modifications.
There are many good used handguns that can be had in the $300-$400 range. Smith and Wesson, Taurus and Ruger double action revolvers in .38, .357, .44 and .45 as well as 9mm and .40 Glocks, decent 1911 variants like Norinco, Browning Hi Power clones and a wide variety of law enforcement surplus pistols that appear from time to time. If I lived in the city I'd go with a Glock 19 in 9mm, but that's just me. There is a lot of decent and cheap 9mm surplus ammo out there. Enough said there.
Ammo is through the roof still, and in short supply. Ammo availability and pricing is a consideration for both handgun and rifle choices but deals can be had on surplus ammo like 9mm and 7.62 in large quantities.
Other good choices for a handgun, particularly for the novice, is a revolver. There are great revolvers that have been made by Colt, Ruger, Smith and Wesson and Taurus, and you can find many gently used examples for reasonable prices. If you're want a handgun that can occasionally be concealed easily, I'd get a snubnose or 3" barrel .38 special. If concealment isn't a consideration, then I'd go with a 4" barrel in a .38 special or .357 magnum, because you can always shoot .38 specials out of a .357.
If I lived in the country, in an area with feral hogs and coyotes, I'd probably opt for a Ruger Blackhawk Single Action revolver in .44 magnum. This being said, I have a friend who regularly hunts hogs very successfully with one shot stops with a .45 ACP compact Springfield XD.
There are tons of rifles out there. Consider ammo availability and pricing. If I could just have one defense rifle, it would have to be a MILLED AK-47 of some variety. Probably with a sturdy folding stock, a aimpoint scope and a flashlight/laser combo. Sometimes, you can find deals on used Ruger Mini-14, Mini-30 or M1 carbines.
There are all kind of great rifles out there chambered for 30.06 and other calibers that are semiautomatic, bolt or lever action but which have smaller 4 and 5 shot capacities and longer barrels than assault rifles. These are great guns too, guns by Browning, Remington, Winchester, Marlin and Ruger, to name a few.
AR-15's and clones are generally gonna cost more than the above, even used, but one never knows when one might find a deal on one to fit it in our price range.
I'd be remiss if I didn't mention the venerable SKS rifle. If you get one that takes detachable AK mags, you've got a great gun, sort of like the Glock of combat rifles. They shoot the same ammo as the AK-47, but are a little bit larger. I've seen some of these for about $350. One of my friends swears he'd rather have 10 SKS rifles instead of a high dollar race gun AR-15 from a custom maker. My friend says he'd just have caches of SKS rifles and ammo all around his house and property. This friend actually owns several high end custom AR-15 guns and does know his guns.
THE ADD ON GUNS
The first add ons that someone would want to add to the above rifle-shotgun-handgun combo is a .22 pistol and .22 rifle. You can certainly find both of those used for under $500, maybe as cheap as $200 to $300 with smart shopping. In addition to being handy to have if you live in the country, .22's also makes shooting practice cheap and for those in the family who don't want to shoot larger guns, well, it's more self defense options as well.
I have a great .22 Marlin semi auto that holds like 16 rounds in the tubular magazine. That's some decent firepower. A Ruger 10/22 with a 30 round mag is another great pick. One of the best .22 pistols I've ever shot was also the cheapest: a 1960's 9 shot Harrington and Richardson heavy duty revolver with a 5" barrel. It wasn't so pretty, but had a good trigger and was very accurate. There are a ton of great used .22 pistols and rifles out there.
Another add on might be a concealment revolver, say a snubnose revolver in .38 special. The gun makers listed above have all made great snubnose revolvers, some of which are very lightweight at 12 ounces. I'd recommend a Bodyguard or Centenniel, and Taurus as many fine offerings as well. Look for deals on old Colt Agents from the 1980's as well, a parkerized and cheaper version of the Detective Special. It's not unusual to still encounter lots of police surplus revolvers from the distant past that are still in excellent condition.
I wouldn't be surprised to see some military auctions of handguns and the like over the next few years. Keep your eyes open for refurbished military and police surplus weapons and the like, which often come with a warranty if refurbished. Also, several Federal agencies are rumored to be changing to Sig Sauer P250 pistols in .357 Sig, and if true, this means there will be a flood of Fed surplus .40 and .357 Sig Glocks and Sigs on the market soon.
Anyway, these are just some of my thoughts on a three gun defense combo. The other thing is, when you do get your guns, stockpile a variety of ammo and have it where you can get to it.