Your domain name is how visitors easily find you online. It is often the first step in getting your website started because it is like establishing your website’s street address on the internet. If you did not have a domain name, you would have to give out your IP address to everyone who wanted to visit your website, which would get confusing and be easily forgotten.
Migration or transfer services are often free or offered at a reasonable fee. These services help move your existing site to the new hosting provider. They can save a huge amount of hassle. Just remember that the migration process is often automated, and may fit in with the host's processes and needs rather than yours. Not everything may migrate, and you may find the organization of the newly migrated site makes for harder maintenance in the long run.
Many services offer so-called unlimited or unmetered service for whatever amount of bandwidth, disk storage and sites you use. It's important to understand that most terms of service actually do limit the definition of "unlimited" to what's considered reasonable use. The bottom line is simple: if you're building a pretty basic website, unlimited means you don't need to worry. But if you're trying to do something excessive (or illegal, immoral or fattening), the fine print in the terms of service will trigger, and you'll either be asked to spend more or go elsewhere.