When pigtailing a second load to circuit

Any spot on the neutral bar for the neutral, and ground bar for the ground, will do.

The connections on the neutral and ground bars should be in the same order as the corresponding circuit breakers.

This is neater and makes fault-finding easier. It might not be required by regulations, though.

As long as that is the main panel, and not a sub-panel, then both go on the same bar. If it's a sub-panel or four-wire, the neutral goes to the neutral bar. And ground goes to ground bar. Look at wires feeding panel; Three means it's a main panel. Four means it's a sub-panel.