Your choice of project topic will be wide. First find a lab that works in the specific area you are interested in. Most academics have more research ideas than funding, so they will be able to suggest a couple of projects to you. If you have your own research ideas, then it can do no harm to ask, but not all research is suitable for PhD projects (they have to have some hope of producing enough results within three years) so be prepared to be flexible. As you are not taking a funded studentship, the research project will not have been peer reviewed, so it is very important to make sure you choose a supervisor with a good reputation.