I think a white shirt wil look to bland and washed out combined with this light colored suit.
Also since it's a summer suit I think navy tie is to prefer before black.
As for shirts, solid light blue, perhaps a gingham white/purple or white/blue. Light lilac shirt would probably work as well.
Regarding tie,,,grenadine or knit, navy for example.
I like that suit, Holdfast. For ideas—see TTO today: blue shirt (somewhat "bluer" than you're wearing) and a navy tie.
Thanks to both of you I'll try something like this next time. Blue shirt with navy tie seems an across-the-board consensus for next combo to try with it.
(MrChris is right that white shirt really doesn't work against the colour of this suit, and I also am not personally much of a fan of black ties in summer)