Which OBD-II adapter should I buy?

The OBD-II standard became mandatory in 1996 for cars sold in US market, 2001 for cars sold in EU market and 2008 for cars sold in the Chinese market. So if you have earlier car, or car sold in other market, please search the internet that it really is supported before you purchase the OBD-II reader.

On iOS:
OBDLink MX+ Bluetooth: Super fast update rate, on a modern car up-to 50 Hz. Has a power saving feature, so it won’t drain your battery if you leave the adapter connected, and a physical button for pairing as a security measure. NOTICE: You’ll need to buy the one with ‘+’ at the end of the model name for iOS, the others will not work. This model has replaced the MX Wi-Fi adapter.
KiWi 3: Not too impressive update rate at 10-15 Hz, but it connects using Bluetooth LE, which means zero user action needed to connect when starting sessions. This also leaves your Wi-Fi available to control other devices, such as your GoPro action camera. Kiwi 4 will work as well, but read this before you buy.
Carista Bluetooth OBD2: Affordable alternative, update rate at 10-15 Hz, connects using Bluetooth LE.

On Android:
OBDLink LX Bluetooth, MX Bluetooth or MX+ Bluetooth: Super fast update rate, on a modern car up-to 50 Hz. Has a power saving feature, so it won’t drain your battery if you leave the adapter connected, and a physical button for pairing as a security measure.
Carista Bluetooth OBD2: Affordable alternative, update rate at 10-15 Hz, connects using Bluetooth LE.

There’s many more adapters that will work, but the ones mentioned are the ones I’d buy. Notice the data rates mentioned are shared between the logged channels. So if you need to log 3 channels, and your adapter achieves 15 Hz update rate, it means it’s 5 Hz update rate per channel.