Unlike the vast availability and selection of tattoo machines you see today, they were once upon a time hand made by a very small group of people. You didn't have options to select from and you got what was available to your geographical reach especially considering that the internet wouldn't exist for a few more decades. The only way tattoo machines from foreign destinations arrived in the states are from tattooists travelling and sailors. Port towns had an advantage of seeing things that inland cities never encounter and you see tattooers from back in the day establish shops in port towns as tattoos and sailors were and still are synonymous (when I was tattooing in NYC, I knew I had rent made when the ships were sailing in, this was true for every shop I worked in near a port). The exchange of information was a very small scale and only between tattooers as it was a close kept secret once upon a time and you had tattooers back then that typically did it all, make the parts and machines as they were not mass produced and tattoo. The parts that were used were on the BBS system (Beg, Borrow, Steal) and they all start as raw material. To give you an idea, the now famed Micky Sharpz dial machine were so-called because it used dials from old British payphones when they were upgraded. The British payphones once upon a time used cast iron for the dials and he (Micky) got them for free since the old phones were simply discarded.
It starts with the parts
Consider before buying a coil set what the core is made of, ideally you want a ferrous metal core (no stainless, no plated) with good electromagnetic conductivity. Most of the coils you can buy today will work but how well? Lets start with considering which is better, a solid core or a hollow core? If you answered solid, congratulations; density certainly does correlate to the produced strength of the Electromagnetic Field (EMF). Coils are mounted by passing screws through the bottom of the frame and thread into the core of the coil. The type of screw you use here will vary EMF (screw should be unplated steel) as well as how far in the core is tapped. Ideally the core should only be tapped as far as necessary for the screw to secure the coil to the frame to take up the mass of the core from being drilled and tapped to aid in achieving the best core density possible to produce as even of an electromagnetic field as possible. A trick to take up space in a coil core that has been over tapped is to stuff it with metal shavings or steel wool. Short of buying heat treated 1050 cold rolled round stock and tapping it your self, I do realize that finding out what a company uses for the core material let alone how it is tapped maybe difficult to come by; this assuming the company that you are buying from isn't outsourcing the core or the entire coil. This is where contacting reputable companies come in, do your research as it really is worth it. I often encourage people to make their own coils as I mentioned earlier how the machines were made onsite by the old time tattoers, well; the techniques of ye olden days can be applied to day. Methods to make coils can be found with a simple search on the web and they truly aren't that difficult to make, they just take time to make. If anything, do your self a favor and make a coil winding jig before trying. As for buying them pre-made, I recommend coils from Pulse International, those ladies and gents at Pulse are very much into the craftsmanship from small parts out to completed machines.
A very overlooked step when building a machine is the coil height in relation one another. The height is corrected by employing one or more various thickness steel shims below the coil on the shorter of the two coils. The idea is to get the coils lined up physically to get them to produce the even EMF for the machine to run as smoothly as possible no matter which way it's held or what kind of resistance it encounters. When the coil heights are mismatched, you will experience performance degradation in the machine and also cause the armature bar to prematurely wear down. An easy way to tell if the coils are at the correct height is by mounting them to the frame and depress the armature bar down, if the armature bar touches one coil and not the other, that would be the higher of the two coils and the latter must be shimmed.
Seth Ciferri machine with coils that I've designed to be phase corrected to produce a very even EMF. Since the coils were designed and fitted to the machine, no need for shims. You can see the tool marks on the close up on the bottom of the cores. They don't have to be pretty, they just have to work well.
By now you wonder the number of wraps on a coil are and which one should be chosen. This comes down to what type of needle you use and what kind of tattooist you are. If you are novice you should stay away from bug pins and use 8 wrap coils to minimize running the machine hot and causing damage to skin until you get more time with a machine in your hand and learn the nuances in tattooing from skin to machine. If you are experienced, you likely have tried various sizes and come to a decision which size suits your needs best as artists often do when deciding which paint brush is needed. Some cases a large wrap coil is unavoidable when using extremely large group shaders (we're talking breaking the 21+ needle group magnums) to have it reliably and evenly deposit ink. Can you run the monster groups with smaller coils? Sure, but just simply not as well. It's the difference when hitting the gas on a four cylinder and a tuned straight six, they'll both go but one just does it better.
I've got some tattoos I need to finish on a few people, it maybe time to come out of retirement for select pieces.......