This plugin will help you to optimize your wordpress database.
Briefly, use phpMyAdmin, which is included with most hosting control panels. More details and links to further explanations are here.
Because it's a fairly safe bet that the core WordPress files will be successfully backed up. Plugins vary wildly in the amount of data that they store. For instance, it's not uncommon for some statistics plugins to have tens of megabytes worth of visitor statistics. These are not exactly essential items to restore after a catastrophic failure. Most poeple can reasonably live without this data in their backups.