Hi there - I have never gigged - Yet!!! BUT Colin if my audience had my taste I would play all the songs you mentioned plus,

Nightingale sang in Berkely Sq
Young and Foolish
When I fall in love
Nearness of You etc. etc.,
My Funny Valentine
Embraceable You
We'll gather lilacs

I would also throw in some rousing Marches to get the feet tapping. - nobody sleeps when you play a March!!! Joan