Book of kels in response to your question to fly international into Darwin you would have to fly Via Denspasar (Bali), or Manila (Philipines) or Cairns via Japan.
In September it becomes the build up before the wet which means you have tempretures of around 35 degrees celcius and around 70% to 90% humidity so hence it really sux. I gather you are from the U.K because of the pound coversion so i would not go to these areas around these times.
A better option would be to fly into Brisbane, Sydney, Perth or Melbourne being that it is starting to get into summer around these places so the weather is perfect.
Having said that if you still want to come to the tropics try to come around January cause the rain will have set in by then and you can see some of the best electrical storms i have seen.
In response to the money easily it is enough to keep you living it just depends you will still be able to go out at least once a week it just depends how much you drink but for food dorm accom and travel expenses easily.
Hope i have been some help ask anymore and i will try to tell you what i know