Is it ok to have Google as my default while using Safari and if so, which browser is supported when doing a search ?

Google is the default search engine for Safari. The user can change which search engine is the default by going to Safari-> Settings->Search->Search Engine. You have five different search engines to choose from. I personally have always stuck with Google because I find it the most robust in finding things. Google Search is far and away the most popular search engine on the planet but some don’t like Google’s penchant for collecting data for advertisers.

Feel free to try the other search engines to see they satisfy your requirements.