What is the minimum set of registers to fill for ADS-B?
ADS-B IN systems do require information from the 0x6X registers. These registers hold information like ADS-B protocol version, system design assurance level and position source quality indicators. 

Without this information the ADS-B IN system can establish a track, but the quality will be flagged as too low to display. 

For reference, get a copy of RTCA DO-260B or EUROCAE ED-102A, whichever is cheaper. They are the Minimum  Operational  Performance Standards for 1090 MHz Extended Squitter Automatic Dependent Surveillance – Broadcast  (ADS-B).