You should be comfortable with both carbide and high speed.
High speed is very inexpensive and OK/Good for many parts. It can quickly be shaped for odd part features like an O-ring groove, a sharp inside shoulder step, turning threads, a certain size radius. most any mild steel, brass, or aluminum parts, and Ok for cast iron, any feature you don't have an insert for.
Carbide tooling is great for repeat parts and harder material, and cast iron.
Understanding how different rake angles and clearance angles affect different materials and cutting forces is very important.
Chatter, poor finish, unable to turn small diameters can be the result of wrong cutting tool geometry (shape), and sharpness.
Most High-speed bits don't need high precision angles, HS turning bits are often just eyeball angles with not even using a protractor.
Thread cutting bits /insert need to be accurate and set to the part accurately.
You can free download How to Run a Lathe by South Bend(better to have your own book).
Tool bits:
https://littlemachineshop.com/images/gallery/instructions/grindingtoolbits.pdf
You can likely practice turning a straight to the size part, turning to a step length, tuning a screw thread. repairing a thread, turning a small diameter part, end facing, putting in a center with a center drill, going to between centers, parting off, tail adjust to make an angle, drilling and screw thread tapping, restoring the tail angle to straight, indicating the OD of a held part, adjusting a 4jaw held part to center, better center a 3jaw part with using shim at one jaw, with the tooling you have.
books:
how to run a lathe book - Search