Some people say rent a variety of gear (e.g.: BCD's) & some say buy up front so all that rental money goes into your gear & saves you money. I favor the latter approach, but one can argue for either. My own thoughts on the gear you'll likely graduate to from here, and some options (not guaranteeing they're the best, just giving some examples):
1.) BCD - most people start out in jacket style. You'll see people post about back-plate wing, which have advantages & are very popular with some, but I imagine you'll at least start with a jacket style. There are a number of reputable brands/models. I dive a Sherwood Avid 2x. I also use an Air 2 instead of an octopus, but that's very much a matter of personal preference. Get weight integrated! You can always wear a weight belt anyway if you want to (which I doubt).
2.) Regulator - you want one an area dive shop can do the servicing on. Some strong brand names include Atomic Aquatics (the Z2x), ScubaPro, Apeks, and a number of others. You very likely do not need a high-end model. An Atomic A. Z2x would be a decent choice, if you want something to check into.
3.) Scuba Boots - I like SeaSoft Sunrays. Thicker sole than regular thin-soled scuba 'booties,' more like wearing a sneaker. Really nice when walking on rough ironshore in Bonaire.
4.) Compass - a Suunto SK7 is a very reputable version. You can get console, wrist or on unit attached via retractor to a D-ring on your BCD, I believe. I've got a wrist unit, but I'd get the last option if I had it to do again.
5.) Dive Computer - you can get a console unit (often cheaper for air-integrated than wrist AI units), or a wrist unit that's got a decent sized display, or small wrist watch style wrist unit, and you can get air integrated (acts as an SPG, costs more money, non-console requires a wireless transmitter attached to your 1'rst stage) or not cheaper. Some dive computers can download dive data to your PC; I highly recommend this to aid logging dives, but it often entails a $100 proprietary cable (may or may not be included). Some models from Oceanic Worldwide: Pro Plus 2.1 (console), VT4 (wrist AI), Atom 3 (wristwatch AI), Geo 2 (wrist non-AI). Some AI wrist units can be bought cheaper without the transmitter. To learn about & compare dive computer, go to DiveNav's web site. They've got cheap online courses to learn to use them.
6.) If you like console units & can cough up $1,100 - 1,200, I love, love, love the easy-of-use intuitive menu system of the Atomic Aquatics Cobalt.
7.) Mail order is usually cheaper than local dive shop. One reputable vendor is ScubaToys, and I believe they offer a discount to ScubaBoard members (you have to mention it. I've also bought from LeisurePro and Scuba.com. On the other hand, there's something to be said for supporting your local dive shop. Some LDS's may offer you a discount on gear you buy related to a course you take with them, and there may be a discount for package deal. So, see what a package deal will run & whether you can get a further discount if you sign up for an advanced OW course. I found ScubaToys willing to substitute a different BCD in one of their packages, by the way.
8.) Get a small BCD knife in case you get tangled in fishing line. Titanium is expensive, but much more rust resistant.
Spyderco has some H1 knives that are said to be rust resistant; still expensive, though.
9.) Consider buying & learning to use the combo. of a finger spool and an SMB (surface marker buoy). It can be hard to see your heads sticking up out of the water from a boat with even small waves & a modest distance, and this inflatable 4 foot orange or yellow tube lets you show them where you are. Good for some peace of mind.
10.) You're going to want to get an Advanced OW cert., both for training/experience under supervision & so charter boats will let you do some deeper dives with them. How old is your daughter? If she's a juvenile, it could impact max. recommended depth limits. You will eventually want to take Rescue diver; it goes a long way to make you a more informed, mindful diver (but you'll need to be First Aid & CPR certified to take it).
11.) Another course you may want, that's pretty quick & can be useful for Bonaire & live-aboards, is Nitrox.
12.) If your fins don't have a spring straps, a lot of people like them & you can add them. Not a big deal, but nifty.
Richard.