That's a rather odd-looking machine concept. Is there a particular reason for those proportions? If you have a special part you're making, and this machine is only designed to make that one thing, then it might make sense, otherwise you might find it limiting when you want to do other projects.
You might want to beef up that long gantry beam in the vertical direction, since it will tend to sag in the middle otherwise.
Actually building the machine first, and then shopping for motors, is generally a good idea. Things tend to change as a build progresses, and you don't want to be stuck with a control system that's not appropriate for the new design. The extra time will allow you to do more research into the various alternatives, and mull over things like torque curves, inductance, and power requirements.