The number of flutes are dictated mainly by rpm and cutter diameter. There is lots of highly technical stuff written about this for milling machine cutters for metal. You'll find it if you search for "feeds and speeds".
A key concept is that you want each flute to dig in and remove a proper chip every time it enters the wood. Too many flutes, travelling too fast with a slow feed of the router through the wood and you will make sawdust not chips, the flutes will rub over the wood instead of digging in and cutting, and you will scorch the timber.
Simple practical observations:
More flutes = finer finish at a given speed and diameter
Single flute = makes and clears a proper chip on very narrow cutters
Two or more flutes are better balanced than a single flute
Three or four flutes are usually found on large diameter cutters such as baseboard flattening cutters. Cost more and give a finer finish.
Straight cutters are cheapest and you can easily touch up the edge with a diamond sharpener.
Spiral bits make a nice clean shearing cut but you can't easily sharpen them yourself.
Spirals may have to be ground from solid carbide making then costly
Downcutting spiral slices cleanly down into the top surface when working with laminated and veneered board. The direction of the shear presses the laminate onto the core, rather than trying to pull it off and leave a furry edge.
Upcutting spiral does the same if the laminate is on the bottom surface and there is a up+down spiral cutter for use on sheet that has laminate top and bottom.
Upcutting bits are good at clearing the chips out of a slot
Downcutting bits may need the router to be positively held down to the work as they create an upward force on the bit while working. Chip clearing is an issue if you are routing slots in laminated board.
Spiral cutters are nicer than straights for non ferrous metals and plastics, but straight cutters work.
HTH
