Recs.
Updated
Pi Zero is an extremely small and cheap (can be found for as low as $5) SBC. It uses a relatively powerful GPU and can support a Full HD display at 60FPS.
SpecsUpdate
Pros
Pro Extremely small size
The Raspberry Pi Zero measures only 6.5cmX3cm and is 0.5cm thick. Making it one of the smallest (if not the smallest) single board computer that can run a desktop OS.
The small size makes it extremely portable and manageable, compared for example to the original Raspberry Pi which often looked clunky and large when strapped on something that would be moving.
Pro The largest and most active community
Raspberry Pi has the largest following of any single-board computer. The amount of guides, tutorials and software available for the Raspberry Pi is unmatched by any other competitor. A regular user has close to no chance to run into a problem that hasn’t been covered already. If a web search doesn’t yield any results, the users on the official forums are very responsive and will usually reply within a day.
Pro Can easily be powered from any external battery pack
Because of its small size and because of the ARM based processor which is extremely energy efficient, it can be run with any kind of external battery pack, even those that are used to charge phones.
This makes it perfect for portable projects that need to be run even when not close to an energy source.
Pro Easy to install the official OS
All Raspberry Pi boards run Linux as a default OS, the Debian-based Raspbian specifically. Setting up Raspbian on a Raspberry Pi is a breeze and even someone who has not installed an OS before can easily do it.
By simply following the official documentation, you download the relevant software on the microSD card and boot up the board. After this, you can simply follow the instructions to install the OS.
Pro Based on the same Raspberry Pi Hardware
Zeroes are basically trimmed down versions of their larger Raspberry Pi sisters. Trimming out unecessary I/O ports and connectivity ports were done to make the factor of the Zero smaller. As of 2018, Zeroes are based on the Raspberry Pi 2 hardware.
Cons
Con No Ethernet port
The Raspberry Pi Zero has no Ethernet port, which means that the only way to connect to the internet with it is through a WiFi dongle, the built in WiFi from Zero W variants, or a USB Ethernet port.
Con Has only two micro-USB ports
Due to its small size (and price) the Raspberry Pi Zero only has two micro-USB ports, and one of them is for power which leaves only one port for peripherals.
Con Needs micro to non-micro converters
Because Zero uses small factor I/Os, you need converters like mini-HDMI to HDMI, mini-USB to USB-A, to work with this device.
Con No built-in Wi-Fi
Raspberry Pi Zero, by default has no WiFi card. This can be circumvented by buying a WiFi dongle or buying the Zero W, which has the WiFi built in.
Recommendations
Comments
Out of Date Pros + Cons
Con Impossible to find one actually selling for $5
Usually out of stock or with shipping fee higher than $5.