Hi. Congrat.s on joining the hobby.
Gear rental can really add up, so if you're going to dive a few times per year or more, especially locally, you'll probably want to buy your own. You will probably want:
1.) BCD - I greatly prefer weight-integrated. Some people on the forum prefer a back plate & wing. I use a Sherwood Avid. There are a number of reputable products out there.
2.) Regulator - will you be diving in cold water at times? Sometimes that impacts preference. You'll want a regulator of a brand that one of your local dive shops can do routine servicing on (likely annually). I use an Atomic Aquatics B2, but there are other reputable brands, such as ScubaPro.
3.) Dive Computer - I recommend getting one that can record your dives & upload them to your computer. Air integrated costs more money but can record your air pressure for the log. Wrist computers rely on a wireless transmitter if air-integrated; console computers don't need a wireless transmitter. I really want the new Atomic Aquatics Cobalt, since it looks great, should be a fine product and most importantly I'm hoping the menu system will be drastically easier to intuitively set, vs. current dive computers that can be like changing settings on a wrist watch. I currently use an Oceanic VT3.
4.) Camera - a lot of people like a brand name point-&-shoot with an underwater case, like the upcoming Canon G12 (figure Canon will have a case for it). Some people like the higher end cases from Ikelite. Some people add external strobes (underwater flashes, often on articulating arms) and may use digital SLR cameras, but you'll probably start with a point & shoot. There are 'dedicated' diving cameras, too, just to confuse you more.
Richard.