It's going to take a while until I get full equipment, but I'm going to keep those things in mind.Three things I would look out for when trying out fins:
1. Length matters. It's like gears on a bicycle or car. If you have much drag in the water, you need shorter fins. Freedivers have the longest.
2. Buoyancy also matters. Fins are at your sternmost station. Choose ones with lower or higher density to cancel out pitch momentum from the rest of your setup.
3. Visibility is also important: If you're in a dark lake, muddy waters and diving with a newby, you want to make it easy for your buddy to keep in visual contact. Use bright colours, ditch the black and camo look.
Edit: One more hint: If you choose bungee straps, keep them out of the sun or regularly change them. UV radiation damages the material over time.
However, I don't think that I can find any shops willing to rent stuff, so I have to make a purchase that I'm absolutely sure of, meaning it's harder to choose.