Well by 'searching' I assume that you are only using a SELECT query, which of all the types of queries, is the safest.
mysql_real_escape_string() is really only going to help with 'data cleansing' in that, it wouldn't allow any characters in the string that would cause mysql to 'burp', such as the apostrophe.
All aside, mysql_real_escape_string isn't a bad idea. If cleansing is what your after, I would consider the following instead:
trim(stripslashes(strip_tags()));
again, in the case of a select query, usually, the worst that can happen is that MySQL doesn't return results, which is counter productive for the user thereby making an intentional malicious act less likely.
In the case of a select query, I would be more worried that a user could query in a way that would cause MySQL to return so many results as in to cause MySQL to lock up.
In your situation, I would look more closely at how to 'tighten up' my query statement (Ex. use the LIMIT clause in the query statement) and not so much the form itself.
-phpORcaffeine