BigPond Direct connection. Other ISPs offer similar services. If you expect a lot of traffic, you could consider a leased line into the Internet. The costs are higher again. Talk to your ISP about this.
Costs change continually and ISPs often have good sign-up deals, so shop around.
Whatever decision you make should be appropriate to the use your website will receive. There are many, many options available and it's probably best to seek the advice of someone who understands your situation and who knows what options are available in your area. Unless you are part of a large organisation which can afford the hardware, software, and monthly connection charges, you're likely to be better off arranging with your ISP to host your website for you. Unless you want to develop skills in maintaining a server, using an ISP to host your website lets you get on with your primary activity - your cultural pursuits. Summary - what you need if you set up your own server to host your website A computer to act as a server.