If someone without any propulsion jumped from a stationary ship in space, how fast would they travel?
The highest a good athlete can jump on the earth's surface, where the acceleration due to gravity is about 32 feet per second squared, is about 3 feet. If the initial velocity from the jump is $v$, then the athlete's height at time $t$ is $vt-16t^2$. This is maximized at $t=v/32$, where the height is $v^2/64$. This gives $v^2/64=3$, or (roughly) $v=14$. So the athlete can achieve an initial velocity of about $14$ feet per second --- call it 9 miles per hour --- and of course in space you'd maintain this velocity pretty much forever.
(If you can jump either more or less than 3 feet off the ground, then, of course, correct the arithmetic accordingly to get your own speed in space.)re
Velocities always have to be expressed with respect to some reference. When we talk about velocities on Earth, it's usually understood that we mean with respect to the surface of the Earth. If an astronaut on the ISS steps outside of the station, her velocity wrt. to ISS is (close to) zero, but wrt. to Earth's surface, it's 7.7 km/s, because this is the speed of the ISS wrt. Earth's surface. Wrt. Sun's surface, she would travel roughly 30 km/s, because this is Earth's speed around the Sun. Similarly, her speed wrt. the center of the Milky Way would be ~250 km/s, and so on.
Along the same lines, when you say "a stationary ship in space", you need to specify "stationary wrt. what?". It will always have some non-zero velocity wrt. something.