I want my client to have the ability to do things like bold, italicize, and hyperlink text, but I would rather them not be able to use some of the other rich text field abilities.
I see from this question that it may be possible using a 'redactor' plugin? Where is the best place to find information on this?
Is it possible for some Rich Text Fields to have more styling capabilities than others?
Redactor is the name of the Rich Text field itself, as this is a 3rd party component Craft has taken great use of!
With Craft you are able to create custom Redactor configurations whereby you have control over which options you would like useable (bold, italic etc), and these can be set on a per-field basis.
Have a look at the Craft site for details on how to set your own custom Redactor configurations: http://buildwithcraft.com/docs/rich-text-fields#redactor-configs
When you edit a Rich Text field in Craft you will see a 'Config' dropdown. These are the files you have created in
craft/config/redactor (see above link for details)