Best Practices for Client Maintenance & Support Pricing Strategies

Hey Lumers - Had a question for anyone who provides maintenance and support for clients. I have a few now that need me for this and trying to get away from "handshake" type of deals into a professional ticketing system - Kinda torn on how to charge for these services. I'd like for new clients to pay an upfront charge, then hourly after? Hate tracking time for myself or have others do it so I also thought of a monthly cost for unlimited requests under a specific predefined scope? Not too sure - Would love any feedback or insight from anyone with experience in this. Thank you!