The basic ESP8266 modules such as the ESP-01, -07 and -12 are small and cheap but not as hacker-friendly as they might be as they're designed to be embedded into a finished device. But there are various modules around that put an ESP module onto a breakout board and provide essential functions such as voltage regulation, USB-serial and level conversion. The forerunner is the NodeMCU which was originally intended as a Lua/NodeMCU firmware development platform but is perfectly good for other environments.
The heart of it as you can see in the picture, is an ESP-12E module that occupies about a quarter of the board and provides nine digital I/O lines with varying capabilities, and an analogue input that can also monitor the supply voltage, useful for battery powered applications. The board itself has two strips of pins that you can connect to directly or plug into prototype board. It fits neatly onto the little 170-pin boards with one row of holes exposed either side to make connections to and this way it's kept safe from shorting to any metal objects on your workbench. On the larger 400-pin boards you're left with plenty of space to add components.
Usefully it has two small pushbuttons for Reset and Flash though as I recently discovered (the hard way, but that's another story), the latest ESP8266 board support package for the Arduino IDE automatically puts it into flash mode. It uses the increasingly popular (since FTDI-gate) Silicon Labs CP210x USB/Serial interface for which you'll need to install the driver but has proven flawless. The I/O lines are still 3.3V but most peripheral devices are happy with that if you give them a 3.3V supply - NeoPixel RGB LED strips for instance.
Intended as a lightweight development board, if you're targeting an embedded application it's ideal because you can switch to using the ESP-12E alone once you no longer need the serial interface and power regulation. For educational use it's just plug and play with enough I/O for many experiments and demonstrations. I'm gradually working through my boxes of sensors and displays testing the libraries with a view to documenting this in the wiki. At the present time it's my recommended starter device and currently available via AliExpress for as little as £3.60 you can't go wrong.