This one is fairly easy for me to answer especially given that a "bug-out bag" counts as one item!
BUG-OUT BAG for sure! I already have a frame pack loaded with 2 bags that would contain a lot of essentials I would need below:
This would cover my basic essential needs such as water, food and shelter as well as some possible medical & miscellaneous needs as well.
DEFENSE
If I had to take only ONE GUN & some ammo, it would have to be my SKS & 7.62x39 rounds. I've designated this gun as my SHTF gun because it's automatic and I have multiple 20 rd magazines for it (though pinned to 5 rds here in Canada, I can simply unpin it as I don't think we'd have to worry about legalities at that point when SHTF lol)
This would cover my defense requirements as well as give me the ability to hunt for meat for additional sustenance.
FISHING I would take my fly fishing pack which are all already in a bag and the rod in a small easy to carry rod case. Fishing is a great supplement for food and sustenance acquisition and most waters contain some fish. So in case there may be difficulty in obtaining terrestrial animals from hunting, we can always catch some fish!
That would be my 3 items and reasoning behind it! Of course additionally, I wouldn't be forgetting to take my family along with me for the ride lol
Once again, awesome topic 
RE: Weekend-engagement topic week 45: Only three items [answer and win hive]