jano wp and woocommerce advanced search is the best plugin for wordpress and woocommerce, autosuggest products and posts search,
OSD Blog Search Widget plugin adds a widget that contains a form for searching blog posts only. Now includes a shortcode with two optional attributes
Fueto is a free, fully-hosted, API-based, outsourced search engine for your WP blog. Fueto wins because we use social signals to rank search results.