I've always kicked them out of the brush and weeds and shot them on the run with a shotgun. A lot of stops and starts and kick a log or brushpile as you encounter them. A lot of rabbits spook if you stop and stand still.
How can you tell if the rabbit is safe for human consumption?
Since I was a kid, they always told me never eat one that has white spots on the liver. Rabbit fever. This website appears to agree:
on rabbit fever
That said, I later lived with a biology professor in my community who specialized in immunology. He said by the time you examined the liver you were probably already going to get rabbit fever if the animal had it. He said just walking within a few feet of an infected rabbit would likely transmit it. He called it the perfect bioweapon--it would infect about 80% of the people who were exposed and leave them sicker than dogs, but deaths were very rare. It could completely immobilize an army.
He also emphasized it's a rare disease now and never discouraged me from rabbit hunting, especially in winter. CDC says only about 200 cases per year and you can get it from gardening and stuff like that as it exists in the soil. too. Search the websites and you'll see them saying wear gloves when dressing and use tick repellants, as the ticks on the rabbit can transmit it.