Welcome Sharpy. You have a wealth of choice for lathes from mini lathes that are good basically just for pens to midi lathes that can do most things and some with swivel heads to bigger things, to big man lathes (I haven't got one... yet). Prices are from about £150 to ... well lots.
It all depends how much you intend to do and that won't probably be how much you do. When I started I bought a lathe and other bits on ebay for £150, the best thing I could have done.. for me. I still have that lathe and its turned hundreds of pens and also have another Axminster lathe. I use the cheaper one most although it is probably on its way out but its served its purpose.
I guess you don't know what you want to turn mostly at the moment so my suggestion would be buy something cheap with the knowledge that you would buy another in a relatively short time, one that would suit your needs.
Just my opinion...