Hi Daniel,
You need to take the pitch of the screw, the force on the 'nut', and the speed that you want it to travel at, into consideration.
What you have shown is a ball screw, meaning that it runs on bearing balls to reduce friction. If you use a simple brass nut on a steel screw, like on a 3d-printer, the friction will be much higher and you need a stronger motor. If you use a nut on a bolt, there is a chance that the whole thing will jam and move erratically due to friction.
The screw pitch will tell you how fast the motor needs to revolve in order to achieve the speed that you need/want. This is the first parameter you need in order to choose a motor.
The linear load will tell you how much minimum power the motor needs to have. This ideal value needs to be increased depending on the friction of the chosen screw-nut and linear guides.
Let's try a pratical example. You want to use one linear guide to move/lift a 3d-printing bed against gravity. The bed mass with a large model can be 2 kg.
You want it to move at a max speed of 100 mm/s = 0.1 m/s.
The screw pitch is 1 mm, i.e. 1 mm per revolution, so the motor needs to revolve 100 times per second = 6000 RPM.
The energy required to lift 2 kg a distance of 100 mm against gravity is:
2 kg * 10 m/s^2 * 0.1 m = 2 J (joule)
The power corresponding to the release of 2 J per second is: 2 J/1 s = 2 W
so a suitable motor for this example would be minimum 2 Watts @ 6000 RPM, but you would chose something larger due to friction, maybe 3 Watts and it can be expected that the motor slows down due to the load.
Another consideration is that the motor needs to be strong enough to get going. It needs a certain minimum torque. A small, fast traditional electric motor typically has a low torque whereas a stepper motor has a lot of torque but is slow. So it is hard to give clear advice without knowing the exact usage case.