Here's my two cents as a new diver. If you intend to dive more than once a year on vacation... buy your own gear. Don't get all bent out of shape about WHAT you buy the first time, just go to the shop if you trust them and have them give you a nice basic outfit. It won't cost you too much (in the grand scheme of things), but you'll have your own gear to become familiar and comfortable with. This will empower you to dive more. Which means you'll be come more familiar and comfortable with your gear, and become a better diver. And you'll dive more.
It's all so related. And you've started with the basics, so by the time you find some item or technology that you want to upgrade to, you'll have earned it. =-)
I'm hard to fit. That made it really helpful for me to buy my own gear. Even if I weren't, though, from what I've seen others go through with rental gear, I still would. It was the right choice for me, in part because I use the gear at least once a month. Decision might have been different had I only planned to dive once a year.
Common advice is to carry regulator and other small expensive items (computer, light etc.) as carryon, but stashing your BCD in checked luggage.
I bought basic equipment that works in cold water from Oceanic, sold as a kit from my LDS (BCD, computer, reg). When flying, I travel with all my gear on my back in an Akona draw-string top backback style gear bag. It weighs in at about 21 lb and contains everything I need for warm water diving except tanks and weights. BCD, fins, mask, reg, lights, skin, etc. It's big -- but no one has ever stopped me from carrying it on. And if they do, it gets checked at the gate (I'd pull the reg and computer out, they are in their own bag) which is safer anyway.
Amy