You'll need to bid competitively on your remarketing ad groups in order for your ads to show on Google's Display network. You'll be competing against all of the other advertisers who are running remarketing campaigns as well as against other ads targeting the Display network. Keep in mind the purchase cycle and your different remarketing audiences as you decide how much to bid on each segment.
You'll need to create a remarketing campaign and multiple ad groups for your different audiences. Creating separate ad groups for each remarketing audience will allow you to better segment and bid separately based on priority.