Can all brands choose between 1P and 3P?

It depends on the marketplace, but the majority of the time the decision is made by the platform. For Amazon and Walmart, 1P is an invite-only program with few new brands being invited. 3P is generally more open and available to most brands. However, Amazon and other marketplaces may place limitations on a brand changing from Vendor Central to Seller Central, while others might have the flexibility to choose.