From David in Israel: On Survival Cycling

It really doesn’t matter if we are thinking slow slide, nuke exchange, or just losing your job: The full or partial switch to a bicycle can be one of the best changes a person can make. DO NOT jump into a decision about buying a bike. It is one of the most personal things you will ever own, if you don’t buy the right bike for you it will just end up rusting in the barn.
As I like to beat into you:
#1 It must be easy to use or you won’t when you are worn out tired
#2 Try not to attract unwanted attention, make it look cheap/old

A bicycle is a balance of simplicity versus features.On one side is a single speed coaster bicycle with closed cell foam inner(not)tubes.
Moving parts: Wheel bearings, chain, crank bearing, coaster hub brake, headset (handlebar bushing), and pedal. Using only 7 moving parts and no pneumatic tires this bike may need repacked bearings and a new chain every few years (barring rust-away) there not much to go wrong. On a simple bicycle like this I suggest a steel frame from a quality brand. Get quality coaster hubs from brands like SRAM and Sturmer-Archer. Chrome or stainless steel chains will resist rust. (Rust robs more performance than almost any other cause.) Durable tires with a center strip will greatly reduce the effort required to travel on road. To get more complicated you could go to something with more moving parts like a mountain, road, or touring bike which make the ride easier by allowing you to move faster or climb hills easier by giving you a wide range of gears. Some features to investigate are disk or rim brakes(hydraulic or cable), heavy duty shocks on the front, seat post or rear suspension, derailler gear shifting (a massive failure point, so only buy the most durable or have spares) or internal hub gearing, toe clip or clipless foot attachment, the list could go on.
Another direction is to choose a folding bike. A folder can also be durable but can pack into a large suitcase size allowing you to catch a ride when available, the trade-offs may be durability or riding comfort and accessory options, I suggest trying out several brands before dismissing this group.
Visit several bicycle shops and find a personal mechanic to help you build your bike. A decent mechanic makes his work a passion and will be able to point out the best solution for your application.
Unless you have money only for food and shelter and nothing else don’t waste money on an Asian sub $40-to-$100 15 speed, they are of such poor quality it will forever remain in reserve at the back of your garage after its first ride (just try to keep it in one gear).
Rather than telling you what to think, spend a while researching this topic for yourself on the web and in bike shops. You may also consider buying a mid-level bike and getting to be a regular rider so you can deciding what needs to be improved before making a big purchase.

Some Points To Ponder:
Where will you be riding (terrain, topology, road type)?
What will you be carrying?
What weather will you ride in?
Ability to upgrade?
Durability of components?
Ease of repair in field?
Comfort on long rides?
Long term resistance to environment (rust,sun,etc)?
Trailer or baggage options?
Lighting and generator options?
Electrical or gas auxiliary drive systems?
Ease of vehicular transport (auto,air,train,bus,boat)?
Anti-theft options?
Tools, availability/stockpile spares, field tools?

JWR Adds: Some flat black and flat rust-brown spray paint, applied judiciously, will make a brand new $400 bike look like an ancient $40 bike in just a few minutes. (It will also cut down on reflective surfaces to make it “tactical.”) However, keep in mind that this will not do good things for your bike’s resale value, in the event that you ever have a reason to “trade up.” So unless you live in what is currently an area with a high rate of bicycle theft, it is probably best to keep your supply of subduing paint in storage and to apply it only after The Schumer Hits The Fan.