I recommend all beginners to woodturning split their budget into three. None of us has an unlimied budget so I find this works quite well.
One third goes on the lathe, one third goes on tools and required equipment - sharpening, dust extraction, PPE etc, and the final third on sundries - wood, abrasives, finishes, glues, and the equipment to use and apply these.
It is a rule of thumb so not hard and fast but all too often I come across students who have spent virtually all their budget on the lathe, and then struggle with cheap tools, often blunt as they don't have a good means of sharpening them.