Boeing suggests a rotation rate of 2° to 3° per second on the 737 depending on variant. Longer airplane variants should be close to 2°/second, smaller close to 3°/second. The slower rate is probably a good guideline for the 900ER and 800 variant, 700 should be somewhere in the middle and 600s at the faster end of the range. Target attitude is usually 12° but depends on conditions. Usually take offs are done using both derated thrust and assumed temperature which leads to low power take offs with a low pitch attitude. Unreduced take offs however, especially on light weight, are closer to 20° pitch.
There is not one rate that suits all airplanes, simply check your FCOM use the correct technique for the type in question. A blanket 3°/sec won't work.