I have basic concept of designing a small forum script for my website but I would love some opinions from the more experienced users here on where I should start? Things like, order or what I should do things, common mistakes that I may make and just any advice on it you may have.
Start simple and add features as you go. Security should be your utmost concern and some way to keep spammers to a minimum.
You could start by copying the miniBB forum script at www.minibb.com and modify it to add any additional features that you need that it doesn't already have. A quick modification to two HTML templates will quickly integrate it into the rest of your site.
That is an interesting idea although, I wouldn't feel right doing that I want to to be my own and having it have a miniBB copyright would be odd.