Woodturning is a popular subset of woodworking, in that a number of wood turners really wouldn't care about any other aspects of woodworking other than turning. There's a good reason for that. First of all, to learn woodturning, all you really need is a good lathe and some sharp gouges, skew chisels and parting tools. You'll need a way to keep the tools sharp so they cut properly, and will want to spend a bit of time learning about woodturning safety, but beyond that, you can go a long way toward becoming an expert at wood turning with little else.
But you'll have to have a good lathe. What constitutes a good lathe?
Begin with the Base:
A good lathe must have a good foundation, and this begins with the bed of the lathe. Whether you choose to invest in a full-size lathe, a mini-lathe for turning pens and other very small items, or a midi-lathe somewhere in between, your lathe must have a solid bed, which is the main horizontal beam across the base of the lathe. This beam, often made from cast iron, needs to be heavy to keep the lathe from vibrating when wood is spinning on the motor. Even the slightest vibration can make turning the part difficult (not to mention unsafe), so resist the urge to buy a lightweight lathe for mobility and instead, find a place in your woodshop dedicated to woodturning so you portability won't be a concern. Ironically, the heavier and more solid the base, the easier the lathe will be to use.
The length of the bed is another consideration.
While the headstock is firmly anchored to one end of the bed, the tail stock on the opposite end will slide along the bed to accommodate the length of the spindle you want to turn. If you intend to turn table legs, you'll need a much longer bed than if you plan to spend your time turning pens and bottle stoppers.
Some midi-lathes have the ability to extend the bed. While these can be versatile, if you will be turning a lot of spindles of up to 36-inches in length, you're better off buying a full-sized lathe with a continuous solid bed than trying to extend the bed of a shorter lathe where the connections between the bed and the extension will never be as solid as a continuous bed.
Lathe height is another concern when considering the base. Typically your lathe's spindle should be right about the same height as your elbows when you stand at the lathe. If the spindle is too low, your back will get sore from bending over all the time, and if it's too high, you will have trouble keeping the tools in proper alignment with the tool rest. If you are unusually tall or short, you may need to consider raising the bed or building a platform on which to stand so that your elbows are even with the spindle.
Head Stock & Motor:
The next consideration is the headstock and the motor. Lathe motors range from 1/8-HP to 3-HP with variable speed controls, ideally between about 500 RPM and 4000 RPM.
Obviously the larger the motor the larger the piece you'll be able to turn, as the motor needs to keep the workpiece turning at a consistent speed. If you intend to turn bowls and spindles, you'll need a drive center and a faceplate that will interchange to hold the workpiece without the tail stock. Additionally, if you want to turn big bowls, your headstock will need to rotate away from the base to allow clearance for the large bowl while still allowing you to use the tool rest. Keep these factors in mind when you shop for your lathe.
The tail stock is simply a rotating pin on the opposite end of the headstock that keeps the spindle centered and rotating evenly. The tailstock should lock securely in place in any position along the bed, allowing you maximum versatility in the types of turning you want to do.
Perhaps the most important part of any lathe is the tool rest. One safety rule to remember when turning is to always rest the tool against the tool rest. There is no such thing as safe free-handing of any cut on a lathe, so the tool rest must be able to be adjusted to any position as needed to lead the tool to the wood, and just as importantly, the tool rest must be able to be locked solidly into that position. A loose tool rest is as dangerous as no tool rest (and maybe more so). If you intend to turn bowls or large spindles, you may want to have two or three tool rests of various sizes that can be interchanged within the bed mount to give you versatility for cutting bowls and spindles.
One aspect of using a lathe that may be overlooked is the placement and size of the power switch. In recent years, many tables saw manufacturers have put large paddle switches on their table saws to allow the user to be able to turn off the tool with their leg if their hands are occupied supporting the workpiece. While this may be overkill on a lathe, because the turner only supports the cutting tool and not the workpiece, it still is important to have an easily-accessible on/off switch that you can turn off quickly if the need arises.