I have my first ever Star Alliance flight coming up in December and wondering which FF shceme I should join. Any advice most appreciated.

This flight is LH ticketed, connecting in Frankfurt with two legs on UA. This intial ticket is a multi-leg:
EDI > FRA > SFO > LAS
SEA > FRA > EDI

Based in Edinburgh.
Fly long haul multiple times a year for a mix of business and pleasure. Travel is both to the Americas and Asia, with some middle east travel likely to come.
Most european travel is point to point with low cost due to convenience.
Tend to stick to SkyTeam and AMS where possible. But I'm primarily cost & convenience orientated when choosing rather than loyalty driven. (e.g. this ticket was £3K with LH vs £4.7K with KLM)
Long haul travel is typically business class.
Miles, I rarely spend them.
Have a preference to connect in Europe vs USA when travelling back to Edinburgh (e.g. one of the european hubs giving me one long flight and one short flight rather than two medium flights with a connection in New York etc.)
By far the most important to me is as much preferential treatment as possible when I need to change a flight or there is disruption.