There may be a lot of options out there in fins, but many people - including myself - think simpler is better in fins. IMO a lot of the "options" out there are more about marketing, trying to draw attention and sell more fins at a higher price, but add little or nothing to the function of the fins. Sometimes they just add more stuff to break. Unless you have a good reason to do otherwise, I'd look at any simple paddle style fins that get good reviews (there's more good ones than the 4-5 mentioned above), and fit comfortably with your boots.
Split fins are a frequent topic of discussion on this board, with a lot of haters. All I will say is, read about the pros and cons of those and try before buying. I think they have their place, especially for people who have joint issues or maybe weak legs, but they tend to be heavy, expensive, and can lack power - which is different from speed. You rarely need more speed but often do need power. They work best with a certain kicking style and generally aren't as good at certain kicks or fine maneuvering. If you're a strong swimmer I don't think you should be tempted by these.
Unless your boots are very thin you'll probably find the same open heel fins won't fit right both with and without boots. And most OH fins will not be very comfortable without boots. However, if you're asking because you're looking at doing both warm and cold water diving with the same fins, there's really no reason you can't use heavier boots in the tropics. While you might not want to pack and wear a heavy wetsuit for a tropical trip, and lighter boots can be nice, heavier boots are fine and many people just do that. Even in warm water, where you don't need the thermal protection, you may still need to protect your feet, especially if you are shore diving or otherwise walking around a lot.
Weight can be a consideration. People that mostly dive cold water often prefer heavy rubber fins like classic Scubapro Jets, as they perform well and the weight there can help with trim/floating legs in cold water gear (not to mention they're bulletproof and inexpensive.) Similar style fins are also made in lighter materials. If you're traveling by air you may want to look at lighter, mostly plastic fins, as the weight can add up. If you do both you may eventually just wind up with 2 (or more) sets of fins and boots. For the same money as one set of the latest fancy gimmicky fins, you could probably buy 2 sets of simple but very good and much less expensive fins, one suited for cold water and one for warm, and be better off.
Spring or bungie straps are popular and make it much easier to get the fins on and off. Some fins come with them now, or you can buy them separately or maybe even make your own.
If you're out to save money, buying used fins can be a great option. It's pretty easy to judge the condition, and the mostly likely thing to be wrong with them is straps, which are easy to replace. The fins I happen to like (original US Divers Blades) are no longer made but if something happens to mine I just find a pair on eBay for like $20.
