I have used default magento search on couple of stores. Can anyone suggest the best extension for this. Also as there are lot of extensions available, how to chose one?
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We've noticed huge increases in search accuracy by Integrating Solr (It's free). You just have to remember you're search is only as accurate as your data and configuration. You will need to invest time/resource into refining your search data and search configuration for your userbase.
MySQL fulltext search is always going to give you fairly poor results unless your data lends itself to really simple keywords searches. Passing your search off to a service designed for the job will provide you with more accurate and valuable results. On MySQL fulltext search we had a catalog of 15,000 SKU's displaying poor and fairly useless results. Adding Solr and specifying which product attributes we want to use for search data gave us an instant improvement in accuracy and increased the usability of the site.
This answer I wrote explains how you can get more out of the Magento default search. It might be helpful in your situation.
Implementing Solr or other enhanced search options can be a big task and you'll need to weigh up the cost of setting it up vs the benefits of your expected outcome. It may be worth revisiting the default Magento search. Personally I avoid third party modules wherever possible, especially in more complicated areas of the framework like the checkout and search.
If you tag your questions with the version of Magento you are using then you might get some more specific answers.
Magento is built on the Zend Framework which also natively includes the Lucene Search Engine.
The Magento install contains all the essentials to have a far better search system than is provided by either "dumb SQL Like" search or the almost better "MySQL Fulltext" search, but sadly the developers never implemented the one item that makes an e-commerce website search function to the level customers expect.
Third party modules are available to turn on Zend Framework Lucene search
From experience, the increased sales paid for the module very quickly.
A nice side effect was elimination of the hate mail from frustrated customers who found the stock Magento search to be highly UNsatisfactory despite using combined "LIKE" and "FullText" and then wasting a lot of time optimizing it, setting up MySQL my.cnf settings specialized to FullText and untold hours trying to synonym stuff to make it appear properly.
The only thing better is SOLR, but it takes some technical setup beyond just installing a module and configuring it.
I suggest you using Advanced Search and Fast Autocomplete for your site
This module has some advanced features than Magento default search such as: