Zero-Downtime Website Host Migration

My current site lives on a shared hosting plan whose renewal fees have crept far beyond what makes sense. I’m ready to move every byte—files, databases, email records, SSL keys—to a new provider without my visitors noticing a thing... (Budget: ₹1500 - ₹12500 INR, Jobs: Database Management, DNS, Linux, MySQL, Performance Tuning, PHP, SSL, Web Hosting, WordPress)