GoDaddy to Cloudflare Domain Migration

I need my primary website domain—together with the web-app that sits on it—moved from GoDaddy over to Cloudflare. The site is running smoothly right now; there are no performance or security problems, and I’m not looking to introduce any redesigns or feature upgrades during the move... (Budget: $30 - $250 USD, Jobs: Cloudflare, DNS, GoDaddy, PHP, Web Hosting, Web Security, Website Management, Website Optimization)