OK I've put myself on the spot there haven't I?
Firstly let me say that I'm not a machinist by any stretch of the imagination. Even though I've had various lathes for over 20yrs there are others here that are far better qualified than myself to give guidance. Another point I would like to make is that any choices you make has to be yours and yours alone.
I believe that at the lower end of the budget you can get a lot more machine for your money in the second hand market.
The main downside is obviously that in that area you will not get a new machine so some wear must be accepted. Vigilance is required in respect of how warn or what may need fixing or replacing.
But, it's my personal view that things may not be a dangerous as it first appears. It just depends on your viewpoint.
Lets say you do manage to secure your dream and it turns out to be a mistake. The machine is junk

You have two options, first is to re-sell and you'll most likely recover what you have spent if you took your time and bought wisely.
You may even make a bonus.
This is because second hand items have a similar value at the time you bought and when you later wish to sell. Something that will never happen if you buy new.
Your second option would be to part the machine out and you would probably make a profit on the sum of parts.
For some strange reason parts are often worth more than the whole.
Anyway, I've yet to buy a second hand lathe that was junk so have never needed to worry about it.
My first mill was junk, but my second and third were good value. Actually my second paid for my third with cash to spare.
My current mill is a Beaver, bit like a Bridgeport.
I'm about to take delivery on a new lathe and I'm afraid you'll have to wait to see what I decided on in the end. I spent about a year searching and deciding on what I wanted this time.
My personal choices were, CVA, Smart and Brown or if I was in the US it would have probably been a Monarc 10ee. Though there are others of course. Just stay away from machine shop lathes and look more closely at toolroom lathes. The former were bought for mass production machining and the latter were very much more expensive new and better made, so were generally bought new for development work.
Funny thing is, most toolroom lathes now fetch much less value of production lathes second hand

Sounds odd but often true.
One of the other big bonuses with second hand is that they often come with expensive extra tooling. Something you often have to add to a new lathe.
Some people buy new from lands far away and certainly this can be a good choice for many. Their reasons are varied, but probably the main reason is time. Most people have jobs, I don't, giving me time to search a deal out but less funds to play with.
Each person will have their own set of criteria to work with.
But you sure do get a lot of iron in the second hand market these days ... nobody wants them, except us and we are only saving them from the scrap man.