Can my headings use one font and the rest of the text another?

Yes. Each kind of text has its own font setting on Settings → Appearance → Font Settings, Global Font Settings section:

• Body Font and Paragraph Font for normal text.
• H1 Font to H6 Font for headings, from the largest to the smallest.
• Link Font and Button Font.

Pick the heading font for H1 to H3 (or all six), and a simple font for Body and Paragraph. Click Submit.

All choices come from your Website Fonts list. The quickest way to get a heading and body pair is Font Presets, which adds both fonts and applies them in one click. Two fonts are usually enough. More can make the store look busy.