A quick overview of metal lathes:
Metal lathes are machines made for making round metal parts. I assume that you already knew that. In electric bass hardware, we use them for making parts like bushings, ferrules, strap buttons, Fender-style barrel bridge saddles, etc. You can also make many of those parts without a metal lathe, using drill presses and files. Slowly, but it works for custom parts. If you have a milling machine, but can't afford a metal lathe, you can do lathe jobs on a mill using a small rotary table. I'll show you that.
However, if you are serious about building up a small machine shop capability, a decent small metal lathe is a must. Along with a small milling machine. With those two machines, you can make almost anything.
There are mini-size benchtop lathes available, which are made for small hobby-size work. Bass-Babe showed her Unimat, which is a high quality hobby size metal lathe. You can also get cheaper grade mini-metal lathes from Harbor Freight, etc. You can certainly make parts like strap buttons and ferrules on these mini-lathes, but it's slow. They don't have the horsepower and cast iron. Peeling metal requires horsepower and cast iron.
Here's my main small metal lathe: A Logan model 1940 from the 1970's.
I bought this Logan in 1990 from a guy who restores machines. With most of the accessories, all cleaned up and tuned up, for $1600. It was my first "real" metal lathe, and it has served me well for 33 years.
It's 11" swing, a 4' bed, about 5' overall. It weighs about 600 lbs, without the custom base bench. The motor is 1/2 HP, runs on 120V. Quick change gearbox for threading, power longitudinal and cross feeds. I have it outfitted with a spindle nose that takes standard 5C collets, and a lever-type collet closer. I also have 3-jaw and 4-jaw chucks and a faceplate to fit it, although I rarely use them these days. I have the aftermarket turret tailstock assembly, the standard tailstock, and an aftermarket lever cross slide. This is an all-purpose small metal lathe, often called an Engine Lathe, capable of doing most small lathe jobs.
The term 11" swing means that you can mount a workpiece up to 11" diameter on it, and it will clear over the ways. However, at that radius, this lathe only has enough torque to make light skim cuts. With 1/2 HP, this lathe is realistically best suited for work up to 2" diameter. I use it only for parts 1" diameter and smaller. But that's almost all bass hardware.
If you are looking to buy a metal lathe for your small/home shop, I highly recommend these Logans. They aren't real fancy, but they are workhorses. Lots of them available on the used market. I frequently see Logans on the LA Craigslist for $500 to $1500. They are easy to work on, and you can still buy parts for them. A company called Logan Actuator sells all the major replacement parts. And there are aftermarket accessories made specifically to fit Logans.
Bigger lathes:
The Logan was my only lathe for a long time, but now I have a few others. Bigger and smaller. My main big lathe is this LeBlond Regal 17 from 1949. It's 17" swing, 6' long, 3 HP, 3400 lbs. This is obviously more than you need for making parts for basses. I have it so I can do larger machining jobs, such as making up parts to rebuild other machines.
However, I do use the Regal 17 for some bass part jobs. Yesterday, I was roughing out a batch of stainless spoke wheel heads for truss rods. The reason is horsepower and cast iron. The Regal 17 can peel off stainless at 5 times the rate of the Logan. Where the Logan was groaning peeling off 0.010" per pass, the Regal was cutting 0.050" per pass, and not even breathing hard. If the part were more rigid, I could have cut 0.100" per pass. That's what bigger lathes are for: Faster metal removal; less time.
When we get into making some round parts in this thread, you'll see me using both the Logan and the Regal 17. The Logan does most of the basic drilling and facing of bass parts; the Regal does the heavy metal removal to save time.
That's enough about lathes for the moment. Let's get into some metalworking!