How do I track where a customer is in my process and trigger actions when their stage changes?

Use a pipeline. Your pipeline is the process, so build the logic around its stages. When you open a contact, the pipeline switcher shows right away which pipeline and stage they are in (for example a proposal stage). You can create your own pipelines with whatever stages you want.

Example for a home inspection business:

1. Create a pipeline with a column for each step, for example Booked home inspection, Home inspection completed, Roof has damage.
2. In the workflow that handles bookings, stop the outreach once someone books and set the contact's pipeline stage to the first column.
3. Build more workflows with the Pipeline column change trigger. For example, when the stage becomes Home inspection completed, email the customer a thank you and send a reminder to someone on your team to write the proposal.