There's an excellent, free pdf article on this very subject at the Mslexia website.
Here's some opening lines of books I own:
White Teeth by Zadie Smith
Early in the morning, late in the century, Cricklewood Broadway. At 06.27 hours on 1 January 1975, Alfred Archibald Jones was dressed in corduroy and sat in a fume-filled Cavalier Musketeer Estate face down on the steering wheel, hoping the judgment would not be too heavy upon him. He lay forward in a prostrate cross, jaw slack, arms splayed either side like some fallen angel; scrunched up in each fist he held his army service medals (left) and his marriage license (right), for he had decided to take his mistakes with him. A little green light flashed in his eye, signalling a right turn he had resolved never to make. He was resigned to it. He was prepared for it. He had flipped a coin and stood staunchly by its conclusions. It was a decided-upon suicide. In fact it was a New Year’s resolution.
Labyrinth by Kate Mosse
A single line of blood trickles down the pale underside of her arm, a red seam on a white sleeve.
At first Alice thinks it’s just a fly and takes no notice. Insects are an occupational hazard at a dig, and for some reason there are more flies higher up in the mountain where she is working than at the main excavation site lower down. Then a drop of blood splashed onto her bare leg, exploding like a firework in the sky on Guy Fawkes night.
This time she does look and sees that the cut on the inside of her elbow has opened again. It’s a deep wound that doesn’t want to heal. She sighs and pushes the plaster and lint dressing tighter against her skin. Then, since there is no-one around to see, se licks the red smear from her wrist.
Room by Emma Donoghue
Today I'm five. I was four last night going to sleep in Wardrobe, but when I wake up in Bed in the dark I'm changed to five, abracadabra. Before that I was three, then two, then one, then zero. "Was I minus numbers?"
"Hmmm?" Ma does a big stretch.
"In Heaven. Was I minus one, minus two, minus three- ?"
Kissing Games of the World by Sandi Shelton
Harris Goddard's life ran out on an otherwise ordinary afternoon in the middle of May, on the very day it seemed thed rest of the planet was pulsating with life. An unexpected warm front had blown toward the coast overnight, pushing out the last remains of the long, wet Connecticut winter and nudging the buds into a frantic, hurried bloom. By 11:00am the thermometer on the side barn read eighty-six damp degrees and Harris, standing on a ladder and scraping the peeling paint off the house, felt as though he might have missed out on the news flash that the world had slipped into the third circle of hell.
- One eventually gets going though the style for me is rather un-engaging.
- For the next two, the immediate focus is the main character involved in something interesting and idiosyncratic.
- For the final excerpt, a dramatic event is described that sets off a chain of events for the MCs.
So, it seems, to be an engaging first paragraph your reader must be immediately led into the meaty details of the narrative.
How does you opening paragraph shape up?