If I could only have one it would be an 18-20" 7.62x51/.308Win. It would be a FAL, AR10, or M1A.
I personally think people put too much glass on SHTF rifles because it lets them shoot better groups. There is a huge penalty in speed and tunnel vision with high power scopes and that could cost you your life. The USMC snipers used 10x scopes to shoot 800-1000 yards for decades. Today they still only use a 3-12x S&B (although the Premier was approved as an 1:1 engineering swap) on their .308s. The longest kill with a .308 was set recently at 1400 yards. The Barret M107 uses a Leopold 17x. Fighting is center of mass. Any magnification above what you need to accomplish that is a liability in SHTF. Thus, I generally recommend you divide your ideal max range by 100 yards and that is the upper limit of magnification. E.g. 500 yards would be 5x.
For most SHTF scenarios I would suggest your engagements would be less than 200 yards as most of your action should be defensive. Since you are asking about only one gun, my .308 would have to fulfill CQB as well. Anything with a lowest magnification above 2-3.5x is too high for CQB IMHO. Anything above 1-1.5x requires a both eyes open and focus on the target to accomplish CQB. It takes training to get your brain to superimpose the reticle, so practice.
On the FAL, I would put a 1-4x on it. Even high end FALs with hand loads rarely hold better than 1.5MOA and with surplus it usually is more like 2-3MOA. Obviously there are guns which will do better, but these are averages. I'm not going to BS you and suggest that a FAL can consistently shoot sub 5" groups at 500 yards just because someone on the Internet posts a 3 shot wonder group. If you can't do it on demand and every-time, it isn't that accurate. I.e. your sample space is too small.
The AR10s and M1As can do much better, but field usable variants still are usually 3/4-1MOA with handloads and 1-2MOA with surplus. Again, you can build a tighter match gun, but unless you are spending really big bucks for a custom job, they tend to not like dirt/surplus/long strings without cleaning. That is the reality for a SHTF gun and IMHO, the necessity for a only one gun choice. Because of the increased accuracy, I would consider moving up to a 2.5-10x NF or similar. I would prefer to keep the lowest magnification to around 2.5x, but allow for more precision shots. I would stick with NF, S&B or Premier, but I'm a glass/quality snob. I would not put a 3-12x or similar large bell scope (40-50mm) on them. Those are best left to guns that don't need to serve CQB purposes. I also would choose a thick reticle, no fine/sniper variants. Definitely mil/mil setup (this goes for the FAL too).
If I was (and I am) biased toward optimizing for 0-300 yards with reasonably engagement capability out to 500-700 yards, I would and did choose a Trijicon 3.5x ACOG with the .308Win drop compensation. I've handed that gun to people had them hit center of mass steel at 700 yards 3-4 out of 5 shots. There are better CQB scopes, there are better DMR scopes, but for all around capability, ease of use and reliability an ACOG is hard to beat for a versatile gun. No twisting turrets or adjusting magnification or batteries. Point and shoot. Always ready.
The best "one gun" solution is to find people who are local to you and complement each other. Combined arms theory. Let people specialize in CQB and mid-ranges/DMR and perhaps a "sniper." The guys in the middle have the best versatility, but the specializations on either end augment the groups capabilities significantly better than adding more do it all guns. Here is how I would set up each person if they only had one gun.
CQB (0-200 yards ideal, 300 yards effective range)
A high quality milspec AR15 with rails (I like Danial Defense), WC TTU single stage trigger upgrade, Aimpoint T1 (battery life is so good this is the only battery powered device I would put as primary), fixed front post, rear sight can be fixed or flip up, Magpul accessories, AAC SPR/M4 suppressor, one point slings, Surefire scout light, eagle plate carrier/LBE.
Mid-range (100-500 ideal, 700 yards max)
Same as the AR15, but 16-18" .308 AR10, 3.5x ACOG with .308 drop compensation reticle, lightweight bipod (weight is a big problem here as a .308 is already much heavier than a .223), AAC Scar-H reflex suppressor, one or two point sling.
DMR (250-600 ideal, 800 yards max)
LRB M1A setup like this, except I would probably go with a 18-20" barrel and a shorter MB/AAC suppressor and a different bipod.
"Sniper" (500-1000 yards, 2000+ yards max
A .308win is sufficient, but I would prefer a .300WM or .338LM. Better yet is a quick barrel change between 308/338. You can shoot machinegun ammo it needed, but really have the power to reach out and touch something. .50BMG while cool, really is specialized and probably only useful in larger groups and against materials. The sniper needs a spotter who should be equipped with a AR15 or AR10/AGOG setup. Also the sniper should consider an AR15 or 12ga while the tactical rifle is carried in the pack.
For SHTF, CQB is more important than max range. I would want at least one mid-range or DMR and then load up on CQB (3:1 or 4:1 ratio) before considering a sniper. Alternatively a several snipers providing firesupport with 4+ CQB would be very effective if you can fortify with CQB and control the surrounding area with the snipers. Your particular locality will dictate the best ratios.
In that case, I'd say an AK in 7.62x39 and a 12-gauge pump. Both can be had for the price of one AR...though AR's are admittedly pretty sweet to shoot.
which is in itself enough to buy one, just to tick off the antis. 
Milsurp brass is plentiful and inexpensive, so reloading's a good proposition. Even the Euro-manufactured Berdan primed NATO ammo is good practice ammo.