Accelerometer selection?
Like most sensors, accelerometers are subject to offset and range errors as well as noise. Each of these parameters usually has a temperature dependence, too.

In addition, since you need to mathematically integrate acceleration to get velocity, there are additional considerations. A constant error in acceleration (because of offset or scale errors) results in a velocity value that drifts indefinitely with time. And the noise in acceleration results in a "random walk" of the velocity value that also grows with time.

There are various ways to deal with these real-world considerations, but it's too broad a topic to get into without knowing more about your specific application.