You'll need to do a few things before you invite people over to view the room you've listed on Trade Me.
Obviously you'll need to tidy the place up, especially the room that's being advertised. Then, get together with your flatmates to discuss what sort of person you'd like to live with. Write a list of questions to ask people who come to see the flat – attitudes toward general tidiness, noise, and smoking are all good things to discuss with people who you'll be sharing space with.
Arrange for the person to come over and see the flat when everyone can be home to meet them. Start by taking them on a tour of the flat and show them what room is being rented, and then get everyone together for a chat.
Remember that the point of this discussion is to make sure you're comfortable with one another and could live peacefully together. Discuss the topics you and your flatmates came up with earlier, and let the person who has come to look at the flat ask their own questions.
Even if they express interest right there and then and seem like they'd be a good fit, consider waiting a day before deciding if you'd like them to move in with you. Thank them for coming over and tell them you'll be in contact the next day. This way you can make sure everyone agrees on the new tenant.
It's also wise to ask for references and check those before you make your final decision – ideally people who have lived with the person. Find out if they paid their rent on time and what they were like to live with in general.