Asking what font to use for h1 and h2 is like asking what color should I use for my background without giving any further information.
Indeed. In the absence of that information, here are a few considerations:
- Is a lightweight mobile compatible page a priority? - Would using images be preferable to a font download? - What kind of business is being represented? - Does it use a particular font that evokes the brand? - What kind of impact is being sought?
My general preference is to specify only super-compatible font families for both text and headings, as I like to keep my own pages as lightweight as possible.
But when choosing fonts for a client, the nature of the business is a major consideration - fonts can be highly evocative, there are thousands of them, and what works for a florist may not be suitable for an undertaker.
The "best" font is the one most suitable for the job in hand.