Urgent: How to plan a seamless cloud migration?

I'm at my wit's end trying to sort out this hosting mess. After hitting resource limits repeatedly on shared hosting, I've finally decided to bite the bullet and move to cloud.

The problem is, I have no idea where to even start with the actual cloud migration process. My site is live, and I absolutely cannot afford significant downtime. I'm terrified of breaking something critical or losing data during the move. I'm desperate to understand the absolute critical first steps I need to take before even touching anything, and if there are any recommended tools or services that make the migration smoother, especially for database transfers. Managing DNS changes to ensure minimal downtime and a seamless transition for users is a huge concern, and I'm also really worried about common pitfalls to avoid during a first-time cloud migration.

I'm completely stuck and really need some expert guidance on making this transition as painless as possible. Any advice, even small tips, would be incredibly helpful right now.