What would be an acceptable sustained (long term) rate of accelleration for a MANNED spaceship?

1G would be ideal as that solves lots of health problems. And in practical terms it's all you need. Skipping the effects of relativistic speeds (time dilation and mass changes close to the speed of light), at 1g in around 365 days you'd be travelling at the speed of light (which you can't do).

So for any long range travel 1G is pretty much ideal.

The space shuttle accelerated at a little over half a g. Humans could tolerate more, but there's no need.

If you start at rest and accelerate at 1g for an hour, you will have covered 63,504 kilometers in that hour. 0.5g for an hour takes you 31,752 km. 0.5 g for four hours takes you 508032km. 1g for four hours takes you 1,016,064km, which is three times the distance from the earth to the moon.

Of course, you keep traveling even after you stop accelerating. 0.5g for four hours takes you to 70,560 m/s, or 254,016 km per hour. If you stop accelerating, you'll cover a little more than the distance between the earth and mars every hour.

And in case you're curious, accelerating 0.5g for 24 hours will take you 36,578,304 km, and you'll be going 423,360 m/s, which is 1,524,096 km/hour. You'll be at mars in under 148 hours.

How long term? If you are talking anything longer then a few hours then anything higher then 1G is going to be uncomfortable.