jbroder - 12:17 am on Jun 1, 2011 (gmt 0)
Databases are fairly interchangeable. So don't worry about it too much.
I could be wrong, but I think the standard is mysql (not mysqli).
Sorry to complicate matters further. :)
If I were learning from scratch, I would just get started on a project. Learning from books doesn't work unless you have a project to make the lessons stick in your mind. So if you don't have a host yet, just pick a host and use whatever database they have. It will probably be mysql.