Website hosting is typically measured in the amount of disk space you're allotted on the server and the amount of data transfer or "bandwidth" you need for accessing the server. For example, if you have a lot of customer interaction at your website, such as files to download, you will access the server frequently and you'll need more Web hosting transfer space than someone who simply puts readable text on their website. The more "items" or "content" you have on your site (i.e., photos, maps, PDF files, etc.), the more disk space you'll need for website hosting.
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.