If you need something a lot more powerful than Better Search, check out Relevanssi (Finish for Relevance). It installs just like any other WP plugin but when you take a look at the control panel, it is truly mind boggling.
It even has a Google style “do you mean” search suggestion as well as Fuzzy matching so it helps users find results better. Like Better Search you can log your visitors’ searches. You can also exclude certain words from being included.
I have decided to give it a whirl here on this site versus Better Search. Let’s see how it does.