I can't give any Emirates-specific advice, but I am a local and can advise that Adelaide Airport is a pretty efficient operation that usually gets the job done right and I'd be amazed if you have any issues there. Taxis from the airport are expensive, as is the 'Skylink' bus, but there is a regular AdelaideMetro (branding of integrated train/bus/tram system) bus route going to/from the city at regular intervals which is much cheaper but not as well advertised.
Feb 2015 in Adelaide = Cricket World Cup? Even if you're not coming for the cricket, January-March is the best time to fly in as there are volunteers stationed at the airport to help with advice for local transport and so on whenever there are major events like the Tour Down Under, Clipsal 500, Womadelaide and so on.
Feel free to hit me with any questions you have about getting around when you're here, decent places to eat out, or about Adelaide Oval if you're coming for the cricket – I go to lots of cricket and AFL matches there and I've worked behind the scenes on the stadium multimedia services during cricket season.