Allow me to expand on the reasoning for my prior list.
For someone just getting in to guns, being the parameters here.
Number One: A Shotgun. A shotgun is the most versatile gun on the planet. With birdshot, it's a bird and small game gun. With buckshot, it's a home defense gun and medium game gun. With foster slugs, it's a large game gun. The gauge should be either 20 or 12, but possibly even 16 gauge. Preferably 12 ga, but 20 will work just as well. The action should be pump or semi-auto, but pump is preferred for maximum reliability. One or two barrels is fine. Two barrels is prefferred (one 26"-28" for hunting, and one 18.5"-22" for defense). If just one barrel, it should be 22" or 24" or possibly 26". Can be chambered for 2.75 only, or 3.0 & 2.75 both. Either one is fine, though 3.0" is preferred, for geese & turkeys. This gun should NOT be chambered for 3.5" shells, IF it's a semi-auto, because reliability becomes compromised with 2.75s. If it's a pump, then a 3.5" chamber is fine.
Number Two: A .22 Rimfire Rifle. This is a close second in versatility to the shotgun. Small game, varmints, fun plinking, target shooting. The action can be any, but strongly prefer a turnbolt, lever, or pump gun (not semi-auto), and a model that can feed shorts, longs, and long rifle ammo. I prefer a turnbolt if I'm limited to one .22 rifle, because they will feed anything and are easy to clean. CZ 452 is an excellent example for this category.
Number Three: A Multi-Purpose/Defensive Handgun.. This gun can serve for concealed/open carry, home defense, vehicle carry, woods carry, or even close-range hunting in a pinch. Can be a revolver or semi-auto; doesn't matter, as long as it's a good design of high quality manufacture. How large depends upon whether you may carry it or not. Barrel length should be no less than 1.5" (revolver) or 2.5" (semi), and no more than 5" (revolver) or 6" (semi). Chambering should be in whatever you can shoot well and floats your boat, but I would prefer .380 auto (9x17), 9x19 luger/para, .38 super, 9x23, 10mm, .45 acp., .44 spec./.44 mag, .38 spec./.357mag, or .45 colt. In particular, I would favor 9x19, .45 acp, .44 special, and .45 colt.
Number Four: A "Full-powered" centerfire rifle. Chambered preferably for a "bottle-necked" cartridge from .243 Winchester to .30-'06 springfield, but a straight-walled round such a .444 Marlin or .45-70 will work too. This is your long range, unusual social problems, and hunting gun. The action can be any (turnbolt, lever, pump, or semi), but turnbolt is preferred pretty highly above all others. However, a lever, pump, or semi will serve well, too. Semi is least desirable because of weight, if you hunt. Preferred chamberings for me, are those with lower recoil, in the 6mm, .25 cal, 6.5mm, and 7mm families.
Number Five: Either/Or The 5th one is tough, and the answer I think depends upon whether or not you're going to be hunting. If hunting is included, then No. 5 should be a muzzleloader in .45, .50, or .54 caliber, preferably in .50 cal. Preferably this ML will be a Savage 10ML, to maximize versatility, if legal in your state to use for hunting, or if smokeless powder ML hunting is not legal in your state, then a true smokepole, either inline or traditional. The frontstuffer is also advocated by some as a good apocolypse gun - if regular ammo and/or components become unavailable, then you could make your own lead round balls, and make your own gunpowder.
If, on the other hand, hunting is not on the list of to-do activities, then I think 5th place is time for a lightweight, intermediate-cartridge, fighting rifle or EBR or HDR or whatever you want to call it - typically an AR15 type or AK47 type, but not necessarily. This is a combination of both a target & self-defense rifle. Highly preferred specific choice here for me would be an AR15 or similar with a 20" HB, in 5.56x45mm / .223 rem - again, great for both shooting targets, introducing noobs, and also self-defense if the S were to hit the F.
I think if you're going to expand to 6, 7, 8, 9, or 10, then it's time to start adding things like (a) extra centerfire handgun (backup, or one for carry, one for home defense, etc.), (b) dedicated "tactical" shotgun, (c) NICE shotgun (O/U or SxS) to impress the boys at the trap club and while social upland hunting, (d) additional turnbolt or double rifle for hunting, particularly one in a DG caliber - over .35 cal, and (e) small-caliber dedicated precision/ varminter rifle, in calibers such as .17 HMR, .20s or Calhoon calibers, .221, .222, .223, .17 centerfires, PPC rounds, .204, .22-250, .220 swift, or even .243 or 6mm rem.
If you go to 11-15, then it's wide open and would include more hunting rifles, more handguns, a big ol' long-barreled revolver, more long-range precision guns, including a .50 BMG, .408 CT, or .416 Barrett, cowboy guns, .22 handgun, more rimfire rifles in both .22 and magnum rimfires, etc.