My lathe has flood coolant built in. It is pristine, has never been used. Flood coolant is the best choice for high performance machining, allows high speeds, keeps the work and tool cool and therefore more accurate, and improves surface finish by washing away the chips. It is also an awful mess, while using it, while cleaning up the floor, and while cleaning up the stinky, rancid mess in the sump. It can also rust machines and tooling. Machine shops use lots of flood coolant, hobby shops very little.
I have a mist coolant system and find it a useful compromise for certain work. The mess is smaller and better contained. You get much of the benefit of flood cooling without all the mess. But it is a compromise.
It is possible to just use cutting oils and other types of "liquid love" which help surface finish, cool the tool somewhat and the work a little. Much less of a mess, much less benefit.
Finally, you can just cut dry. On some materials, with the correct tools, speeds, and feeds it works just fine. On other work you get an awful finish and hot parts and tools and more wear and tear of cutting edges.
All of these methods can be shared between machines with the right equipment.
It is pretty easy to try out everything except flood coolant, which takes more of a commitment. See what works best for you...