Should I start with a gaiwan or a teapot?

Start with a porcelain gaiwan (100–150ml). It's neutral (doesn't absorb flavor), works with every tea type, cheap (€10–25), and teaches you to control temperature with timing rather than thermal mass. A teapot — especially yixing clay — is tea-specific (clay absorbs flavor, so you dedicate one pot per tea family). Once you know which tea you love, then buy a clay pot for it. Skipping the gaiwan and starting with a fancy clay pot is the most common beginner mistake.