The good first sentence is the only sentence
Most readers decide in the first ten words.
If the opener doesn't hold, the rest doesn't get read. The middle paragraph could contain the answer to a problem they've had for years. They'll never see it.
The first sentence is not a courtesy. It's the entire negotiation.
The cost of a mediocre first sentence is everything that comes after. The cost of a great one is the hour you spent writing and rewriting it before you wrote anything else.
Three rules I run on every piece I publish:
The first sentence should be the most interesting sentence in the piece. If a later sentence is better, swap them.
The first sentence should not promise anything the rest of the piece can't deliver. Hype openings are a form of theft.
The first sentence should be short. Long opening sentences are throat-clearing dressed up as authority. The reader knows.
A good test: read your first sentence to someone who has no context for the piece. If they ask "what's this about?" the sentence failed. If they say "tell me more," it worked.
Most writers I admire spend disproportionate time on the opener. Many of them write the opener last, after they know what the piece actually says.
I do this too. The first sentence is usually the hundredth one I tried.
The reward for caring about the first sentence is the only reward that matters in writing: someone keeps reading.