The trade-off
Storage is access versus cost versus counterparty. Home is near and on you. A vault is distant and on them. Allocated means specific bars or coins in your name; pooled or unallocated is a claim on a stack. This page describes the menu. It does not pick.
Home
Home storage keeps the metal in your control and the operational risk on you: fire, theft, forgetfulness, and the fact that a safe advertises itself. It has no vault fee. It has no auditor. Whether that is acceptable is a household question.
Allocated and vaults
Allocated storage, done properly, identifies bars or coins as yours. You should be able to name what you own. Unallocated and “pool” accounts are easier to run and easier to confuse with a bank deposit. If you cannot point to a bar list, you have a claim, not a pile.