What are the most expensive coins in the world?

Could you elaborate on the most expensive coins currently in circulation, and perhaps provide a brief overview of their value, rarity, and perhaps the factors that contribute to their sky-high prices? Are they primarily coins from historical periods or modern collectibles? Are they gold, silver, or perhaps a different precious metal? How do investors and collectors typically acquire such coins, and what advice would you give to someone interested in starting a coin collection, especially if they're aiming for the most valuable pieces? Thank you for your insight into this fascinating world of numismatics.