Both these possibilities are well explored in the Expanse series of books (and TV shows).

If a ship is always under thrust, people inside will experience the equivalent of gravity. Humans need gravity (as evidenced by issues of returning astronauts).

If you had a VERY efficient fuel source, you could remain under thrust throughout your journey except at the mid point where the ship must flip (i.e. accelerate at 1.0 g for half the trip and then decelerate for the second half and so have almost constant gravity). This uses a LOT of fuel though so is not practical with any known propulsion system.