If you have static pages (i.e. created in HTML) you won't have any problems and you can select any host provided they meet the disk space and data transfer.
However, if you have dynamic pages and lots of traffic, you may have to go for a VPS (virtual private server). Most hosts advertise 1500GB of disk space, etc. but in actual practice it is not possible. A dedicated server with 160GB of disk space and 2000GB of transfer costs about $150 a month. Shared hosting accounts are also hosted on the same server. How can one expect 1500GB? And that too for $10/month?
This is called "overselling". And about "unlimited hosting", this simply doesn't exist.