In a recent thread on another forum, there were a few very intelligent people on either side of the debate of would they rather have a table saw or a band saw first.
As a turner, unless you are doing segmented work, I see little use for a table saw, most of my turning related work is done on the bandsaw. And if you have a good miter gauge and properly tuned blade, you could probably be able to do segments to, but you might need a mitered shooting board for this.
With A well tuned bandsaw with a fence and a crosscut sled (yes, bandsaw crosscut sled), and a variety of blades for different uses, there is very little you can't do. If you are comfortable with hand tools (planes in particular), then is almost nothing you can't do with a bandsaw. A bandsaw is arguably the most versatile tool in the shop.
With only a bandsaw, sandpaper and finish, you can literally take a rough log to a finished product. Add a few more simple tools and there is very little you can't do.
The biggest key with a bandsaw is tuning it. I am far from good at tuning my saw, but I get close enough to get acceptable results. There are many excellent guides and videos on the net about how to properly tune a bandsaw. Do not expect it to be tuned right out of the box, each time you change blades it will need retuned.
If it doesn't come with a fence, build one, they are simple to make. They are only a L shaped piece of wood that only has to be square to the table, then clamp it down.