Critical steps to migrate DNS from ISP to Cloudflare with minimal downtime

[AbigailLW]

I'm the IT administrator for a small business with about fifty employees, and we're currently using our ISP's default DNS servers, which have been unreliable lately with slow resolution and occasional outages. I want to take control of our DNS management by migrating to a more robust provider like Cloudflare or Google, and potentially setting up a local caching resolver on our network. I'm comfortable with basic networking but haven't handled a full DNS migration before. What are the critical steps and common pitfalls when changing DNS providers for an entire domain? I'm particularly concerned about minimizing downtime for our website and email services, and ensuring all our subdomains and MX records transfer correctly.