The airfare / online airline ticket business is extremely competetive and the big players are..well, big. They have tons of money and the latest technology.
You'd need to be able to really provide something unique in order for your website to prosper.
Conceivably you could develop a meta-site: A real-time comparison of the cheapest tickets from the other "cheap tickets" websites, then make some affiliate money. This would require some pretty advanced technology I imagine, although I am by no means an expert.
Whatever you do, plan it carefully before investing a huge amount of time let alone money..
Good luck!