Hello Octo
I've done this trip in almost every conceivable way over the years, but things are constantly changing so there's no avoiding trawling through the booking sites to find a good deal.
As mixture says, Emirates is likely to have the best business-class deal, and when I used this route a couple of years ago, the stop in DXB wasn't too long. Also check Etihad and Qatar, although when I last looked the schedules weren't great (long transit stops).
Best if money is no object is SQ via Zurich; Swiss is also OK but doesn't seem much cheaper.
For premium economy, Air France may be the best bet - I've done a couple of trips to Asia with them recently (with some misgiving), but was pleasantly surprised by the premium eco product (much closer to business class than the eco-seat-wth-extra-legroom offerings of some other carriers), and the prices were very good. Downside is the transit at CDG, but this does seem to have improved somewhat recently.
I dream of the day someone starts a direct flight from GVA to SIN (or another Asian hub), but sadly it doesn't seem to be on the cards...