Step 1: Different types of tooling
HSS Tooling can be very versatile and economical, especially if you don't plan on using the lathe very much, or you don't know what kind of parts you will be making. HSS square blanks are around 4$-7$ depending on size (From KBC. Tools), and pre-ground tools can be found for around 20$-30$ (From Mcmaster-Carr).
However, while HSS tooling can be very cheap initially, it can have drawbacks. Mainly, if you're not a professional, chances are grinding tools will take you significant time, and your tools will not always the same. HSS tooling also has a significantly shorter lifespan than other types of tooling, especially in hard materials.