You should first start off with shared hosting (a small plan).
And then continue to upgrade as you need.

If you grow out of shared hosting, you can either transfer to Semi Dedicated Hosting or a VPS. Personally, I would suggest SDH since you do not have to manage anything and it is alot better than a VPS.

Then you can also continue to upgrade, until you can get your own Dedicated Server.

To start, I would suggest going go the Shared Hosting section in this forum and researching the best host. Do not go with any hosts who have been around for less than a year, do not go with hosts who have outrageous prices, and do not go with hosts who self advertise in this thread. (as you will get many!).

If you need any help picking a host, efel free to contact me