A fin is an extension of the diver, so needs to match his or her physique. One with a large rigid blade requires real muscle power to drive, a bit like riding a bike in top gear all the time. If you are appropriately built, you might be able to handle it. Lesser mortals should look for a fin with a progressively flexible blade.
Current fin technology favours a blade design that allows the centre section to flex further than the edges, keeping the water channelled down the centre of the fin.
This principle is well demonstrated by the Mares Avanti range and the Technisub Idea 3.
The extra-long fins you may see come from the spearfishing culture and are not well suited to normal scuba diving. They are also a real pain in the boat.
The foot/fin interface needs to give a firm and comfortable fit, with no wobbling or slack. If you are only ever going to use your fins for snorkelling from your yacht, a shoe-type fitting will be fine.
Otherwise, the combination of dive boots and adjustable strap fins will prove more practical.
Adjustable fins come in fewer sizes than shoe-fitting fins, so make sure you try them on first, while wearing your boots. Some drysuits are fitted with wellie boots that will force you into the largest-size fins available. Here the fit becomes extremely important, because of the mighty leverage produced by a large or long blade.
Most manufacturers now use quick-release buckles. If you need to remove your fins before getting back into a boat, or walking up the beach, you will want this feature.
Almost all fins these days are made of some type of plastic compound, sometimes combined with rubber inserts. Plastic does not keep its looks as long as rubber and scratches easily.
The fins that disobey almost all of these rules are Force Fins from California. They are shorter and wider, made from expensive polyurethane and have a fairly narrow strap. The most surprising thing is that they seem to work. Perhaps all the others got it wrong.