search engine recommendation needed

I have a dynamic database-driven web site using PHP/MySQL on Linux. I need
to integrate a search tool that will search both the database and static
pages and output a list of links corresponding to the search string entered.

I am an experience web developer, but have never worked with web site search
engines before. I have looked around some and there seems to be a large
variety of solutions. I'm on a small budget (isn't most everyone?!) so
either a free open source or reasonable one-time license is required. I need
something that's easy to configure and auto indexes when new content is
added--either to the database or static pages.

All comments/suggestions welcome.

Thanks!