You need to contact OCBA to register your intention to marry (Notice of Intention to Marry) which must be done at least 30 days prior to your wedding no matter where you have it, and get the appropriate paperwork sorted. http://www.ocba.sa.gov.au/ They are the government department where all BDM's are dealt with.
If you wish to marry on a beach you must contact the relevant local council first. They have rules about large gatherings and I know that Onkaparinga Council require an official application if over 30 people will be gathering for a ceremony on the beach. It's really a rubber stamp thing for them but they DO need to be informed. You'd probably need to have an alternative venue available too, just in case the weather is grotty.
Alternatively the Register Office itself in Grenfell Street has a lovely wedding room. We got married there two years ago next week, and it's just fine. It can hold up to about 60 people I think. When we got married there the total cost was around $180 - and that covers the NOIM, the ceremony and the official wedding certificate and another posh one for framing! You don't get to choose your celebrant at the Register Office, you just get whoever is on duty, but they are all lovely - I met a few during my dealings with them trying to sort out hubby's Prospective Spouse Visa. And of course they are only open Mon - Fri, so no weekend weddings there.
If you use a celebrant they can do a lot of the paperwork for you, but they can be very pricey if you are on a budget - depends what kind of wedding you want.
The first thing you should do is read through the wedding regs on the OCBA site.