On which side should I generally measure my blood pressure, left or right?

Here, we have to distinguish between upper arm and wrist devices.

With upper arm devices, it is in the beginning recommended to perform several measurements on both sides. It is very important that these measurements are all performed under the same conditions. All after a relaxing period, in a sitting position, without talking and so on. If the average of both sides is higher on the left or similar to right, continue your measurements on the left arm. If the average of both sides is higher on the right, continue your measurements on the right arm.

Wrist devices are designed for the measurement performance on the left wrist, only.