Welcome to the forum and thanks for the PM. I'll try to address your questions here to the best of my ability.
When I get a new (meaning very old & very used - even abused) winding machine the first two things I check out are:
-----The overall condition of the machine mechanically. With the machine unplugged and off, I check for broken or missing parts, seized parts, binding parts, gear lubrication, broken gears, bent shafts, sleeve and ball bearings, proper oil levels in such equipped models, etc, etc.
-----The overall condition of the machine's wiring. With the machine unplugged and off, I look for cracked wiring, proper fuses, frayed wiring, loose wires, burnt wires, etc, etc. And repair or replace as needed. Caution some electrical components, like capacitors, can contain lethal voltages even with the power off and the unit unplugged...Only do the electrical inspection and repair yourself if you are qualified and knowledgeable to do so.
Once I establish that all is well with the machine, I also inspect the motor and drive belts in the same manner. I know some winders here actually take the motor to a "Electrical Motor Repair Shop" to have it checked out before powering up. The same safety rules apply here as stated above.
You must also understand how the machine operates and the safety features & protocols of each different type of machine. Know the mechanical features of the machine and how the traverse systems works. Know the parameters of the machine's operation. On some machine brands a wiring diagram is extremely helpful if not a requirement.
If everything checks out and with a good understanding of how the machine operates, AND still with the unit unplugged & power off, I try manually rotating the drive shaft to see if anything is binding. Rotate only in the direction the machine is designed to operate as some machines only wind in "Top-Going" or "Top-Coming" directions. Some can operate in both directions. Operating a machine in the wrong direction can damage the machine and/or the counter. If everything still checks out, I try to power up at a very slow RPM and increase gradually if everything is still good. Know how to shut down the machine quickly in case of emergency. When inspecting any winding machine internally, and taking any parts off, make sure the machine is unplugged and the power is off. Always observe proper safety protocols keeping hands, fingers, hair, sleeves, etc away from any moving parts and electrical parts/connections. Always wear the appropriate eye protection.
Most people's experiences with the Metoer ME301 as noted in various threads here in the forum, include replacing the Friction/Drive Disk. DO NOT operate your machine with a damaged or missing Friction Disk. DO NOT turn the knob that moves the friction disk while the machine is not running. Check the two plates that the friction disk touches for damage or scoring. Fortunately you maybe can buy some replacement parts from a couple of sources (see Meteor's web site and Start - Wickelmaschinen - see Thread called "My New Winder" here on the forum). Do a Google search for Manuals for the machine and see if you might find one. IMO a manual is very important to have when working on any machine.
This forum also has several people that use, and some even recently purchased, the ME301. "basscu" and "rdur" are recent examples and might be willing to share some information and resources with you. Throbak's Jon Gundry is a member here and he has a nice write-up on the ME301 on his web site http://www.throbak.com/me-301-guitar-pickup-winder.html
Your machine visually looks to be in very good condition and hopefully on deeper inspection will prove to be the same.
Hope this helps... good luck and keep us posted.