Staying up is far more important than winning a cup but staying up enables you to become more competative and therefore compete to win cups. But this is a steady process, at the moment we're on Premiership survival!
Well there's different priorities based on a clubs position anyway. A club like Arsenal get Champions League every year - but they haven't actually won anything for a while. I'm positive their fans will want to win anything soon, but relegation is not something they have to contend with - we know it's not really going to happen to a team like Arsenal. Their fans don't start the season thinking " I hope we can stay up". For a team like us (Swansea), avoiding relegation is the main objective. If in a few seasons we are still there and established in the premier league, then yes I would place a lot more interest in winning a cup. This doesn't mean I don't want us to progress in the FA Cup - I hope we go all the way - it's just that the tears I would shed in being knocked out of the cup would be crocodile tears, whereas relegation from the Premier League would seem like the end of the world for me. It's just such a high being in the premier league that I couldn't face the cold turkey of playing teams like Doncaster (no offence) week in week out after playing Premier League sides.