+1 with the other replies. A VERY open question.
Lathe models typically have designations e.g., 1624
The first two numbers are the "swing" and the second two are the "max distance between centres" also sometimes called the bed length.
Spindle turning vs bowl turning is an important consideration.
For spindles you may want a longer bed.
For bowls you may want more swing. The bigger the desired swing, the heavier lathe. Swing is 2 x the distance between centre of the headstock and the lathe bed. So a 12in swing lathe only has 6in between centre of the headstock and the bed. This can be reduced further if the banjo height gets in the way.
Many pen turners are happy with a 12in swing.
Note the max distance between centres is without any method to chuck (hold) the wood. Whatever method you use, e.g., spur, scroll chuck, live centre will reduce this length considerably.
I was not wanting to have to make a firm decision on spindle vs bowl so I went with a lathe with 16in swing and a 24in distance between centres.
I did purchase a bed extension for my lathe but have not used it yet.
So far I have been happy with the capacity of my lathe.
The big surprise in getting into woodturning was the cost of the "accessories". This is the first large machine I have purchased where the out-of-the-box configuration cannot be used without additional purchase of at least a turning tool.
My friend commented "Yes you need to purchase turning tools and these are expensive, at least $30 a piece". I replied I had not purchased one so inexpensive.
The turning tools can be specific to spindle vs bowl work. Another surprise.
In addition to the turning tools is the need to sharpen them - unless you purchase the more expensive carbide insert tools.
I soon found out I wanted to use a scroll chuck to hold the wood. Another expensive item. The scroll chucks take different size jaws. More expense.
I needed a better live centre for the tailstock. More expense.
We are not wanting to put you off, just make you aware that the budget side is an important consideration.
A couple of recommended videos.
This one by Mike Peace is long about 1 1/2hr, but for a person getting into woodturning, this explains the many methods of chucking wood. Any project you do on the lathe requires that you hold the wood in some manner. In many cases there are different methods needed throughout the project.
This would have helped my learning curve if I had seen this at the beginning.
A 6 part series on sharpening by Gary Gardner. This is the first part. I think most of us have some tools which need sharpening.