We four have been diving all over the Caribbean for 15 years, but we only go once a year, in the spring.
RENT: We only dive once a year, and want to avoid the maintence of owning a reg and tank. We also like to travel with only our carry-on luggage.
The regulators that dive shops rent get used every day, so they can be "beat up." The Dive Master on the boat from Sunset House fixed the sticking regulator the one time we ever had a problem. We are like sightseers underwater, and so find the crummiest fins are more than adequate. I mean, we are not practicing for competitive swimming.
OWN: Diving since 1985 myself, and since 1993 with family, we ended up buying four things.
1. Personal dive computers worn on the wrist. If you only buy one thing, ever, this should be it.
2. Our own wetsuits for personal taste/comfort.
3. BC vests for safety. As Rescue Divers and Master Scuba Divers, we believe that it is a safety issue to dive with a BC that has torn or missing buckles or weight systems. Also, it is safer to dive with a BC with which the diver and buddy are VERY familiar. (i.e. where is the extra reg hooked / how is it attached / how do I release your weights / where is your flashlight / how can I get this dang signaling device unhooked, since I can't see it/ and so on)
4. Prescription masks. Self-explanatory.
Rent gear, and dive with, shops that are recommended by your local dive shop, or that are endorsed by PADI or NAUI. A cheaper place that is unknown may not be the best idea. Diving safety is like driving - everybody who does it well appears to be casual about it, but there are dangers if one is careless. When deciding whether to buy or rent, think about what you personally need, rather than follow a list from a magazine or shop. How often will you dive, what do you know about the technical maintenance, and what are you willing to carry.
Hope this helps.