Alex
At that price range all you'll find are second-hand or toys!
"Mini lathe" covers a multitude of machine definitions according to who describes it, you really need to think through just what size machine you need and what materials you want to work in. If you are turning masts and spars from wood then think more in terms of machines for wood rather than the far east "mini-lathes" which are really aimed at metal working. If you DO want to machine metal then that will be another thing to factor in. Without being rude to anyone – or hurting feelings – the accuracy demands for machining masts and spars are totally different to those required for making pistons and cylinders for steam engines and could be met within your budget by careful consideration of just what you want to do. Don't dismiss old machines, while they may no longer be able to keep the accuracy and precision for "engineering" they will still be capable of giving good service for less demanding tasks. The main issue will be that generally they don't operate at high enough speeds for wood turning though, and the bearings won't take kindly to being pushed that fast, but if you can live with the speeds that they will run at, you'll most likely get a far more robust and rigid machine – and rigidity is important for good work.
A lot of the older machines from the early 20th century were made for turning both wood and metal and accessories for both types of work were available. If you go that route you'll probably become VERY familiar with EBay. Don't dismiss that route too quickly all my machine tools have come through that route and I'm happy with them, but I do have a background in engineering so I'm willing to trust my own judgement to decide if a VERY second hand, used (and probably ab-used) , worn machine is worth buying for ME – I'm NOT making aerospace components!
Good luck in your search, a lathe really is a VERY versatile machine, with ingenuity it's amazing just what you CAN machine on them, milling becomes a possibility as well.
Keith