Second-hand versus new?
The problem with second-hand is the 'good make' matters very little if the machine is badly worn or spent 5 years stored in a damp cellar! Condition is everything, and judging it from a position of inexperience can be difficult: an unpromisingly grubby antique might be in better nick than a well-polished jobby covered in fresh paint, but is a knackered machine reconditioned by Coco The Clown! Before buying it, I'd want to see the lathe put through it's paces – nothing like cutting metal to reveal problems! Not much protection if the seller is uncooperative.
This car is a 'good make' and cost a lot of money new – would you buy it now?

New from a UK supplier comes with consumer protection so the thing can be sent back if a lemon is delivered. Slight problem is hobbyists typically can't afford to buy a new industrial machine, so we troop towards Far Eastern Hobby machines. Plenty of choice, especially size, delivered by a nice man, complete with most basic accessories, and a good chance it will work out of the box. If it doesn't send it back. However, the machines are made down to a price, perhaps less than 10% of the cost of the industrial version, so relatively lightly built, rough finish, and reduced inspection which might allow an important defect out of the factory. If this happens, the mistake is fixed by replacing or money back, not by guaranteeing all will be well at all times by requiring all new purchasers to pay a hefty inspection surcharge.
After far too much dithering I started with a Chinese mini-lathe. Light enough to be lifted by a fit man, OK on an ordinary table or bench, quiet, and big enough to tackle small and medium sized work. Does all the usual basic lathe stuff including screw-cutting. Not ideal for clockmaking or big enough for motorbikes, but comfortably good enough for 60 or 70mm diameter and up to 250mm long.
I learned a lot from mine, including how to spot what's good and bad about lathes! I had a notion I would upgrade to an ex-industrial or ex-educational machine once I knew what I was doing. In practice, my mini-lathe's main fault was being too small, not being riddled with Far-eastern faults! So I upgraded to the biggest lathe and mill that would fit in my workshop, chosen from a catalogue, and delivered a week later. All of my Far Eastern machines worked straight out of the box. Both lathes benefited from minor fettling, but the milling machine needed no work at all. Worst item by far was the 6×4 band-saw, but replacing the blade and an afternoon spent filing worked wonders. Despite being rough as old boots the saw works well. None of these machines is suitable for hard production work, but they all do more than I need.
I wouldn't buy a Far-eastern machine other than from a reputable UK supplier. Not because machines from other sources are all rubbish, but because buying direct from China, or from a box shifter, or an opportunist could be admin trouble if a dud arrives. One 'bargain' I looked at required rejects to be shipped at buyer expense to a depot in Germany – not cheap or easy! ArcEuroTrade get plenty of positive customer feedback, and I had no bother with Warco when an expensive item went missing in transit – they just sent another. Searching the forum by supplier name will reveal who gets most kudos and brickbats, but in general all the main British suppliers do the right thing in the end.
Not really about the make in my view, more about condition and what happens if you get a wrong 'un. The make might even be a disadvantage: Myford lathes are so well thought of they attract premium prices, even in poor condition. The reputation is well deserved, but they aren't the best British lathes ever made: at the time, affordable rather than top-of-the-range. I'd rather own a second-hand ex-educational Boxford, provided of course it was in good condition.
Whatever you buy, manage expectations. Lathes don't automatically cut metal perfectly just like that. The operator has a lot to learn, so ask on the forum.
Dave