You have not provided any details on the target requirements and very few on the actual design of "the machine". From what I see so far, it looks more like you are afraid of shadows than trying to solve any real problem.
Let's start with basic. The FCC part 15 in US and IEC 61000 / CISPR 32 standards in Europe are most common documents that govern EMI/EMC. So, before you start asking questions you should decide on what class of device you are making and what kind of standards it should conform to.
Now, the standards define two kinds of EMI, radiated and conducted.
The conducted EMI is usually dealt with by filtering on the power supply and data lines and have nothing to do with shielding.
To suppress radiated EMI you should first identify potential sources. Since you did not mention any high frequency radiating components your biggest concern would be those stepping motors, their power wires and switching circuitry. Note, that they also contribute heavily to conducted EMI. It is rare to see shielded motor cables. The usual approach is to add ferrite rings and lots of bypassing capacitors where necessary.
Another typical source that you did not mention is power supply. These are heavy polluters and unless you are designing your own, it pays to find properly certified part from reliable supplier.
Comparing to the motors and power supply, the digital signals are usually insignificant and easy to deal with using proper enclosure. The noisiest are typically oscillators for MCUs and DC-DC converters. This is where you have to focus your EMI-reducing efforts.
As for data lines, it is important to understand that shielding of digital connections is not meant to protect environment from the switching noise, it is to protect data from the environment. There is no reason whatsoever to shield these inside the enclosure. If you peek into any modern certified consumer device you will rarely find any shielded connections. Most likely it will be antenna coax or mic-level audio. For any external shielded connections (e.g. USB or long runs of load cell cables) the typical approach is to place sockets on the PCB and then mount PCB right at the enclosure openings. In some cases small boards are used with pre-amplifiers or transceivers that convert signals into something less susceptible to the noise that can be further routed to main PCB with unshielded wires.
For the internal connections, if you have multiple data lines combined in the same cable, the best approach is to use FFC/FPC with standard non-shielded connectors while making every other wire a ground conduit. For the differential signals a simple twisted pair should be sufficient. Again, this is to protect from interference within the enclosure, not for EMI reduction.
Finally, if your "the machine" has mains power supply, then proper grounding will go a long way in reducing radiated EMI.
