My battle with drupal's form
Drupal's Form API is complex but gives you lot of things: is secure, is extensible, is themeable. Indeed is more difficult than coding a simple HTML form, but with a simpel HTML form you have a simple functionality: just that simple HTML form.

Form API generates the form HTML element and handles the POST requests, and validate and submithandlers, you don't and you shouldn't code your own HTML form. 

I recommend you to read the Drupal 6 Form API Quickstart Guide. Drupal 7 form handling is pretty the same, but check the Drupal 7 Form API Reference and Form API Internal Workflow Illustration.

In the other hand you may prefer to use a module that address what you need without coding, that's a faceted search: Facet API. From its documentation page:


  Faceted search allows our search results to be filtered by defined
  criteria like category, date, author, location, or anything else that
  can come out of a field. We call these criteria facets. With facets,
  you can narrow down your search more and more until you get to the
  desired results.