There are two possible models, the UTXO model and the account model. Each has advantages and disadvantages. Bitcoin chose the UTXO model. XRP and Ethereum for example use an account model.
What are the advantages and disadvantages of each model?
The primary advantages of the UTXO model are simplicity of implementation and improved privacy.
With the UTXO model, transactions just consume some UTXOs and create some UTXOs. This tight constraint on what transactions can do makes transactions simpler and easier to execute in parallel.
The UTXO model also improves privacy by making it more difficult to associate transactions issued by the same party.
The primary advantages of the account model are improvements in transaction flexibility, account management, and multi-currency capabilities. A transaction in an account model can do much more than just consume and create UTXOs, it can modify persistent data associated with an account. This permits functions like order books and cross-currency payments.
Perhaps most importantly, it allows an account to be managed. For example, the XRP Ledger permits accounts to change their cryptographic credentials. You can have a publicly known receiving address and change the key needed to spend funds sent to that address without having to communicate a new address or move funds.
On a multi-currency system, accounts can specify assets that they're willing to accept as payment. So, for example, if I owe you US dollars, I can check your account settings to see what assets you accept for dollar payments. The enables the XRP Ledger's foreign asset system, enabling the largest decentralized exchange in the world.
Lastly, an account model makes it easier to bring new servers up. The number of accounts will generally be much less than the number of UTXOs in a comparably sized system. This means less data needed to bring on new nodes.