Originally Posted by cougar

For non-RNAV departures, there is no requirement for automation of any kind (A/P, FD, LNAV etc.).

For RNAV 1 departures, AC 90-100A, item 10 provides guidance for flight crew operating procedures. It states in paragraph (9): Pilots must use a lateral deviation indicator (or equivalent navigation map display), flight director and/or autopilot in lateral navigation mode on RNAV 1 routes. Lateral mode guidance should be engaged no later than 500 feet.

AC 90-105 covers RNP 1 departure procedures, and the flight crew guidance is the same as RNAV 1 departures.

Furthermore, both AC 90-100A and 90-105 state:
For normal operations, cross-track error/deviation (the difference between the RNAV system computed path and the aircraft position relative to the path) should be limited to ± ½ the navigation accuracy associated with the procedure or route (i.e., 0.5 nm for RNAV 1, 1.0 nm for RNAV 2). Brief deviations from this standard (e.g., overshoots or undershoots) during and immediately after procedure/route turns, up to a maximum of 1 times the navigation accuracy (i.e., 1.0 nm for RNAV 1, 2.0 nm for RNAV 2), are allowable.

While autopilot isn't required for an RNAV or RNP procedure, it might be a good idea depending on the departure, as some now include RF legs.

RNAV 1 departures require the accuracy of RNP 1. However RNP 1 departures, in addition to the RNP 1 accuracy requirement, also have a containment of RNP 2 (2x the RNP) and a crew alerting and monitoring requirement. This containment width is what the used for terrain clearance.