While Brisbane is usually the most convenient and economical port of arrival for intercontinental travellers, Gold Coast Airport is well-connected with direct flights to most major Australian cities, as well as destinations in New Zealand and southeast Asia, so it's usually the best (ie cheapest) option if that's where you're coming from or headed. Backpackers and other budget travellers should also note that getting to Gold Coast Airport on public transport is only $3.60, compared to more than $30 to Brisbane.
For most visitors the train really won’t be that useful for getting around the Gold Coast itself, where buses are the backbone of the public transport network. Though the regular services between the Gold Coast (Nerang, Robina or Varsity Lakes stations) and Brisbane which take just over an hour are great way to get up and down the coast, while the train also connects the Gold Coast with Brisbane’s domestic and international airports. For the cheapest fares pick up a go card and travel during off-peak times (Mon-Fri 8:30 - 15:00 and after 19:00, plus all day on weekends and holidays) and bear in mind that a separate operator owns the Brisbane Airport stations so there is a premium for airport connections. Check the timetable and which of the Gold Coast’s stations works best for you at jp.translink.com.au.