For home use, you are unlikely to have 3 phase power supplies, so just think single phase.
My preference would be for the 0.55Kw motor, and to make up a countershaft. Probably you can buy pulleys (Picador springs to mind.)
Your lathe is old, very old, likely to be over 100 years old, but still capable of reasonable work, in the right hands, and in fair condition..
Your lathe is almost certain to have plain bearings, most probably the steel spindle runs in the cast iron Headstock, so speed will be limited. 700 rpm will quite fast enough as top speed, and and fairly frequent oiling.
How high is the centre from the bed?
In UK lathes are usually referred to by centre height, such as “3 1/2″ which means that it could swing work up to 7″ diameter. The centre distance is the maximum distance that can be obtained between a centre in the Headstock and the one in the tailstock, say 15”
Our American cousins describe lathes by the swing and centre distance, such as “7 x 15″
It does not have a graduated dial for the Cross Slide. Once it is operable, I would suggest making one.
Just a plain disc would allow you do what the old timers did, which was to put a pencil mark on the disc, and then nudge the dial slightly, take a cut, before measuring the workpiece again. It may be possible to make slightly crude graduations.
Firstly, you need to measure the pitch of the leadscrew (How far the tool advances for one turn of the handle (Rotate the handle by 10 turns and measure how far it has travelled. The pitch, will be 1/10 of that distance. It would be nice if it was 10 t p i (threads per inch.) if you could make 100 graduations, each division would be 0.001″ There could be times when you wanted to work to that level of precision.
If it is 8 tpi, 25 graduations would each be 0.005″ (The thickness of a human hair approximately)
How do you graduate a dial?
Ideally, turn the disc so that it has a circumference of 100 units of distance, such as 3.183 ” diameter or to confuse things, but keep things to a more sensible size, 31.83 mm. Having made a mark, using dividers, make another mark 11 mm away.
Then using that mark, make another 11 mm away, (11 will be easier to set than 1 mm) . Keep doing this until you have 100 marks around the rim of the dial. Then go back and make every tenth mark longer, and then make every fifth mark of a length between the units and the tenths.
There are more accurate ways of graduating a dial, but you do not have the equipment, or at this stage, the experience to use it.
The dial needs to be fixed to the leadscrew, so needs a boss, with a thread tapped into it for a grubscrew to clamp it to the shaft. The ability to unclamp the dial, and move it, makes it resettable.
You need to find someone who is willing to help you; preferably nearby.
Is there a model engineering club near to you?
If so go and join. You will get face to face advice and practical help, to back up what you have read in the books.
Once the lathe is up and running, do not start trying to make things, at once. Just start learning the basics, like being able to turn the handwheel slowly and steadily, either to move the Saddle along the bed, for turning, or the Cross Slide across the bed for facing. Just practice by turning and facing bits of mild steel to get the feel of the lathe. Once you have the dial graduated, just take cuts of 0.005″. You will find that the diameter has reduced by 0.010″!
For measuring, you need something like a digital calliper. Keep and eye on LIDL or ALDI, from time to time they sell them for about £10, Get some spare batteries at the same time. They always run out on a Saturday evening!
The four jaw chuck is a useful item, but will not self centre. Each jaw can be adjusted to bring work as close to on centre as you wish, or as far off centre if needed.
But you will need to learn how to do this, and for real accuracy, needs measuring equipment, such as Dial Test Indicator, and Magnetic Base.
If you could find a 3 jaw self centering chuck, life would be a little simpler, but you would need help on choosing and fitting a suitable chuck to the lathe.
Although described as self centering, a 3 jaw chuck will not hold work ABSOLUTELY central, it is likely to be, even with a good one, eccentric by about 0.003″ Poor or worn ones will be worse! I came across one that was over 1/32″ eccentric! But there are ways round even that degree of error!
It may seem that there is a lot to learn, but you are entering a field that is completely new to you.
My very first lathe was home made and powered by my pistol drill, so not all precise! But It sufficed to turn a bit of broom handle to align the clutch on a car.
Every step, no matter how small, is another up the learning curve.
We all had to start once!
Howard