Hoping to add a site search to my TAXA website

Right now, the only way readers can search for anything in the wood 
botanical tree I have built is by botanical (scientific) names:
         www.prowebcanada.com/taxa
Most people would wish to find woods and information about them by 
their common names
or perhaps other search terms such as by country they grow in and 
other search choices.
I hope to be able soon, therefore, to install a general site search 
engine that can search
through all the MySQL files being used to store all the data --- 
hopefully one that is free code,
using PHP and downloadable from the Net.

Do any of you have favorite site search software you would recommend? 
Other desired criteria include:

         - All pages are dynamically driven. The search application 
does not have to search
           pages much because all data that shows is stored my MySQL 
tables in a database
           simply called 'taxa'. It needs to do its searching from 
within those tables.

         - Question: At some stage (setup?) would I have to specify 
every table it should look
           into? Could I also use different searches for each area 
(eg. for species, for genera,
           for families, etc.)

         - PHP source code should be readily available in case I need 
to modify something.

         - I work on windows at home but the website is on a Linux 
account at GoDaddy.
           The software must therefore be independent of working only 
on Windows.

         - I have 6,500 records for the species table but that will 
expand well past 12,000
           eventually. The site search has to be able to handle that 
and more. Many of the
           programs on the Web talk in terms of how many pages but 
that does not make
           as much sense here as searching through thousands of records.

         - Preferred: For setup, the simpler the better.

I took a quick initial look but am willing to bet that someone in our 
group has one or more
favorite, proven solutions.

I look forward to your suggestions :-) .

Bill Mudry
Mississauga, ON