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Don't rush into a purchase. Find a local M E Club and join. You will learn a lot.
Study the many posts on the Forum which refer to mini lathes, and those powered by either brushed or brushless motor.
Both brushed and brushless motors, deliver their power to the lathe via a belt..
My mini lathe is relatively old so has a brushed motor driving by a belt,into a "High / Low" gear choice
Motor speed is selected electronically, give the spindle speeds shown on the digital read out..
The motor speed will most likely not be that of the spindle speed shown on the controls (Motor speed will be different by the gear (belt ) ratio between the motor and the spindle.
Power is fed ton the DC motor in a series of pulses, the frequency of which is determined by the control board speed setting.
As the motor speed is reduced, so will the power delivered (Which is why torque and motor speed is increased; in the same way as a gearbox in a car ) .
As I understand it, the more modern mini lathes are powered by brushless motors, (Where electronics take over the job of feeding current at the right time to the rotor of the motor, to provide the required spindle speed.speed.
Brushless motors deliver a more or less constant torqued over their speed range, meaning that, like most all electric motors, they draw more currents as their speed falls. One of the laws of physics!)
Continued running, at low speed and high current draw will cause the motor to heat up and possibly suffer damage
Control boards have become more reliable, but the best way to safeguard the control board is ALWAYS to turn the speed control to Zero before either staring or stopping (A motor starting up can draw much more than the normal running current, and shutting an electronically controlled motor from speed might produce voltage spikes that can damage the control board. Better safe that sorry.
As a newbie, you need to buy and study an study at least one of the books on lathework
Basic Lathework by Stan Bray, Lathework by Harold Hall, The Amateur's Lathe by L H Sparey (Old and heavily orientated towards the Myford ML7. The details differ, but the basic principles remain the same )
David Clark, Dave Fenner (Like Stan Bray, and Harold Hall previous editors of Model Engineers' Workshop) and Neil Wyatt has written a book featuring the min lathe.
Neil Wyatt has written a book on lathework, based on his recent experiences with the mini lathe's bigger sister, the SC4..
If you want to learn more, please visit our website rotating pneumatic cylinder.
The essential thing is to grasp the basic principles of setting up and operating a mini lathe, and to learn by making simple tools. Not only will such things give experience of the machine, and machining, but confidence in using the machine.
Do NOT expect perfection out of the box. (this is where having knowledgeable friend close by to advise, help and demonstrate
Even a brand new machine may benefit from a little fine tuning..Sadly some machines arrive with built in faults (So so bad that machine has to be exchanged! )
You are at the very lower end of the budget hobby market
High precision COSTS! (A high precision Swiss, industrial bore gauge can set you back $5,000+ after a six month wait!l) An industrial machining line can easily cost MANY millions of £.
Do not expect, even a new, 3 jaw chuck to hold work absolutely concentric. (I have only once found such delightful chuck ) It is more like that a good one will hold work concentric to better than 120 microns (0.012 mm)
BUT correctly set up and used, incredible work can be produced (Witness the model seen at Exhibitions )
For maximum concentricity, or to hold square, octagonal or irregular work, you will soon find a need for a 4 jaw independent chuck (which then shoe the need for Dial Indicator m( ms ) and a magnetic base.
But you don't have to have everything at once.
As you learn and gain experience, you will, eventually become aware of greeter needs., so cross one bridge at a time.
Your budget does need to allow for measuring equipment, cutting tools and very possibly, a bench grinder.
Again, the books will advise on what to but, and how to use for a given job.
Complicated models from expensive kits and material can come later when you know nor about hot to operate the machine.. Spoiling a bit of mild steel bar is far less of a problem that if the workpiece is an expensive casting!
Hope that all this rambling will be of some help.
Howarfd
To answer your first question, "belted" power lathes go back thousands of years and are still in use in aboriginal cultures. I got to see one in action in South America where an Indian was turning an arrow shaft which he had wrapped with a piece of animal gut attached at one end to a convenient tree limb ) bowed down and the other end to his big toe and the shaft was trapped in some low hanging limbs when he pulled down with his toe, the shaft rotated in one direction and when he lifted it, the opposite direction. Using a chipped stone edge, he proceeded to very quickly work the shaft to the desired size and went on down the jungle path. Later. civilations used water mills to rotate shafts and transferred the rotation to overhead leather belts Still later (during the Industrial Revolution) we moved to steam driven shafts and still later (late 's) electric motors replaced the steam engines. (Still overhead belt driven machines) In the early 20th century we started seeing gear driven machines which were more compact. (still belt driven between the motor and the gearbox) To your second question which is better, they're both excellent systems but it really depends on what you want to do with the machine. If you're looking to a general purpose machine ( like the 13X40 lathe) buy the best you can afford. Don't be lured by cheap as you'll get exactly what you paid for. Buying a high quality used machine in good condition would be my choice. Weiler, Logan, , Hardinge, Takisawa, Mori-Seiki ( Yes they actually made small toom room lathes) As my Hardinge HLV-H is a belt driven variable speed machine I can tell you that the belt system is very, very smooth. All gear driven machines without exception have some degree of vibration/ noise associated which their operation. (Although they're still very accurate and robust) For general purposes, I would have to go with the gear driven machine.