This is a very important thread and a matter I have given much thought to
Personally I never feel like bitter cocktails after a large meal - so I tend to have them beforehand (martini, or negroni). It does slightly depend on what you are ordering - an espresso martini goes well after lunch IMO. The LPGS is a signature element of flying First though so I can't resist starting with a glass or two when I arrive!
I tend not to mix the fizz with food - so I would usually move on to a glass of white with my starter, and either a different white for my main or red, depending on what I am eating. If I am feeling particularly luxurious I will have a mini tasting session at the bar first to pick what I want with my food and see what I find delicious (though I can often guess in advance).