Why not create great automations for each stage of your pipeline?

Create each stage automation first, then start them, then you can select which automation is best matched to each of your pipeline stages

Then when you drop your lead into each stage, the linked contact will be added to that automation.

 A key thing to consider is if you have a campaign for each stage, A, B, C, D, E you will want to add an action to B to 'Remove from A', an action to C to 'Remove from A' and 'Remove from B' and so on.
In this way the contact doesn't continue to receive any information not relevant to them and their stage of the pipeline.