If you want to get a collection of good ideas from your team, avoid using brainstorming. Brainstorming means everyone puts forward ideas in a group meeting, but people will often focus on the ideas presented so far (herd mentality).
Instead, use the nominal group method.
Each team member writes lots of ideas on paper about the topic (either before the meeting, or at the start). Once everyone is done, the coordinator should list all the ideas on a board so everyone can see them. This means all ideas get shown. Then you can discuss ideas, or vote on the best.