You run the packs on HIGH when you need maximum cooling. On the ground with the APU feeding them, the HIGH setting gets an extra boost (ca. 20% more flow).
The APU can´t be "overtaxed" - it will reduce the bleed automatically to stay within EGT limits.
To start engines you will always turn both packs OFF - it is possible to run one pack and start, but it is not allowed. You need a minimum of 30psi pressure to start an engine.
You can (we called it Sommerschaltung) close the Isolation Valve once the right engine is running and use that engine to power pack 2 - while starting engine one. The 737 is notoriously bad at cooling in the summer, so every extra second cooling flow helps.
Cheers, Jan