Lewis,
About three years ago I decided I wanted to learn to turn bowls but I wasn't sure where to start. I did a lot of research on the internet at first looking up types and prices of lathes. After I decided on the size lathe I wanted/needed to start with I had to narrow down the brands until I came up with one that was within my price range that had most of the features I thought I needed. Likewise you will need to figure out what you want to turn, what is the minimum size restraints that will satisfy you for now and see how deep your pocket are. This can take a bit of time so don't get impatient. Lots of people in this newsgroup can help if you let them know your intent.
What I wasn't ready for when I first started turning was all the other extra things that add up in cost. You need a good set of turning tools. You need different tools for spindle turning than you need for bowl turning. Yes, there is some crossover at times but the basic tool for bowls is a good bowl gouge. When I first started I bought an eight piece set of spindle turning tools because I didn't know the difference. What I really needed was a bowl gouge. There are several schools of thought on types of bowl gouges to use for turning bowls but you will figure that out later.
Once I got my lathe home and I had the correct tools to use I soon figured out that the tools need to be sharpened, often. Sometimes several times per project. So, you will need a decent slow speed grinder. You don't need to buy the best on the market but you do need one. There are attachments that you can get to make your grinding easier. You will know in time if you want or need one of these attachments but they are not necessary right away.
You will also need a way to hold your work on the lathe. How you accomplish this will also depend on what you wish to turn and how much you want to spend. There are both expensive and inexpensive ways hold your work on the lathe. The inexpensive ways work well but are not always obvious to the beginner. The expensive ways are more convenient but can really cost a lot.
Lastly you will need to gain some knowledge from others who have gone before you. This newsgroup is a good source. The have helped me a lot in the past. But you really need to be able to see someone else turn. Buying video tapes, DVD's and books is a good idea. Bill Grumbine's video is excellent for learning to turn bowls. Richard Raffin's stuff is good. He has videos and books on bowl turning and spindle turning. There is a ton of good material by various turners out there to choose from. You will find that everyone has there own technique and there is more that one way to accomplish many turning tasks. I found it confusing at first to listen to too many people that had different ways of doing things. You may need to pick a person and listen to them for a while until you get your feet wet. Then adding other turner's information will help you gain knowledge. Taking a class from a teacher is also a good idea. After about four or five months of turning and getting frustrated I took a class from my local Woodcraft store. Several of my questions were answered at that class. BUT after a while I needed more. About a year later I took a three day class from David Ellsworth. It helped a lot. Start slow. Turning has a long, steep learning curve.
The moral of this is that turning is addictive. It will always cost you more than you already have and you will never run out of new things to learn. If you have an idea of what kind of turning you want to do then post a message on this group. You will get a lot of helpful infomation.
Hope this helps. Good Luck.