In general, you can use any serif or non-serif fonts for your website heading. For my website (which I had designed and wrote HTML/CSS in 2012) I had chosen Times serif font for the heading. The content is with the non-serif Helevetica. Those worked well and having different fonts for heading and content felt fine for me. The overall effect comes from a combination of heading, borders, and colors. I my case content too had a preference (as it was technical in nature and not a business).
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In general, you can use any serif or non-serif fonts for your website heading. For my website (which I had designed and wrote HTML/CSS in 2012) I had chosen Times serif font for the heading. The content is with the non-serif Helevetica. Those worked well and having different fonts for heading and content felt fine for me. The overall effect comes from a combination of heading, borders, and colors. I my case content too had a preference (as it was technical in nature and not a business).