A real handy tool for this kind of thing is Firefox with the Firebug add-on. It lets you inspect a page and find out all the css selectors and properties, inheritences, and so on.
There could be some variation between themes and TikiWiki versions. I'm not sure what you mean by generic template.css. In the themes I've done for Tiki 2.0 (formerly named 1.10), I've generally been specifying #sitesearchbar, input#fuser, select[name="where"], and input[name="search"]. But now we find that [name="..."] isn't valid CSS so those will be changed, I guess. Also, the stylesheets usually have info for non-specific input and select, so these can have an effect on the search form so should be checked.