Research Proposal for PhD - Rude or Good
The first point to consider is whether you have a prospective research area in mind. Ideally at this stage you should have some specialisation, and a general idea of the field out would like to enter. If this is the case, it makes sense to write a proposal reflecting your interest. Don't make it too specific, but let it show that you have done your homework.

On the other hand, if you are unsure and open to exploring different fields, first select the groups you would like to join, see what work they do. Find a common area of interest and write a proposal based on that. This means you could potentially be writing many different proposals for different universities. The focus would be to ensure that the proposals are relevant to the audience in each case.

Either way, my opinion is that you should have a proposal ready. When you first contact the supervisor, you needn't attach the proposal, just convey your interest to work with him/her, mention some areas of interest and attach a CV.