Seems like folks need some help creating the basic construction of the machine. My first one was made with less than $60 worth of parts, the rest of it was junk bits I had laying around. You can see it in the picture files. A dial gauge indicator and Square will help keep things accurate.
You want the linear rail to be absolutely as square as possible to the bobbin mount / "lathe" part. You can either use collects, chuck jaws, rings with grub screws. Now the X motor, which is the bobbin mount has to have as little runout as possible. I used pvc and pex tubing with double sided sticky tape for weathering windows to make the first layer.
For the base I started out with a pine board and aluminum L brackets, which now I am using a combination of 2020, 2040 aluminum extrusions which are either purchased on amazon or any cnc/3d printer maker store.
The motors, I started with NEMA 17, which is fine, later upgraded to NEMA 23- both were open loop as I had bad luck with closed loop types but supposedly closed loops are better.
The drivers pololu style are not the greatest, but it's what I used to begin with which later became logic level driving DM542T, they can run off a 5v signal- if you choose to use a raspberry pi, you will need to purchase TSX0108E logic level converters that are high speed, and bipolar so they can convert RPI's signals to the appropriate voltages.
100uf (V rating should be 2 to 3x the value you plan to run the motors at, I run mine at 20v, so 50v tolerance) decoupling caps is advisable, you can use an arduino CNC shield.
Not necessary but I like to do is braid/twist the GND and respective driving signal wires together to keep noise down. You can strip an old usb and use the braided coax over as a sleeve and tack it to earth ground/chassis. I would not advise using the wires within the USB as they are meant for 5VDC and low wattage. Ideally you want 26AWG braided wire to run the signals to the motors.
Loctite blue can help keep things square and prevent vibration from rattling a grub screw loose. A heat gun that can reach 550f will break the loctite if you need to disassemble for any reason.
Tension is important, if you can get the appropriate AWG magnetic tensioner, do it. Mine is for 42AWG to 37AWG, however if you cannot what I used with my starting setup was 2 felt discs, a wing nut, 2 washers for the pre-tension/wipe stage, second stage I used a simple spring and pulley through 3 pulleys to straighten and keep tension. Finally an old ice fishing pole's tip, about 8" with a threaded rod and spring that can adust how hard it will pull back up/recoil.
You want to feed the wire from the spool sitting upright so it feathers the wire off the spool instead of unrolling it on bearings otherwise you'd need to tension the spool as well adding unnecessary complexity. Besides, it's how all the professional coil winding companies run wire off the spool. Static, and on a post.
The HMI display was chosen out of convince, it only needs 2 wires RX/TX to communicate, and 2 to power/ground which take up absolutely no pins and it still can be connected to USB as long as you define the pins in the sketch to not conflict with the USB. You could easily make a GUI to run the RX/TX info on your computer/laptop instead of an HMI if it is within your skills.
The power source I used is an adjustable lab bench supply which allows me to adjust voltage, limit current and has overall low noise and protections an otherwise dangerous linear supply would. One could disassemble a semi newer junk monitor or TV and use the 32v and 5v taps assuming you know what you are doing.
The feed arm, I used a simple metal pivoting arm on the linear rail and a U bend of mains copper wire with the bottom smoothly polished and somewhat flattened. Other things that work are a V notch cut into metal, a window seam tool roller, or possibly a V cut bearing with a quarter sanded down. A rigid titanium needle with a ruby coated funnel also will work assuming you smooth out the channel and it doesn't strip enamel off.
This is the basics, if anyone is confused, has any questions or needs more information just let me know. All the wiring is straight-forward and the pinout is in the sketch. The more solid you can make the machine with less pitch, roll, yaw slack/runout. The better your coils will turn out.