If industry-leading uptime and rapid-scalability are your two biggest concerns, cloud hosting might be just what you're looking for. Cloud hosting will get you access to a cluster of servers from which you can quickly provision resources when you need them. Along with having enough separation from unruly neighbors, your application should be kept safe. VPS and Cloud services are sometimes combined into a hybrid service called Cloud VPS or Scalable VPS.
Moving to another website consists of transferring the website’s files and databases, configuring your site with the new host, and directing your domain’s DNS to the new host. Once you pick a new site host, they can usually help you out with this process. The cost will depend on the host you’re switching to, but it will probably be anywhere from $150-$400.