ERC20 tokens are linked to an Ethereum wallet under the hood. That's because ERC20 tokens operate on the Ethereum blockchain. It carries smart contract information that identifies it as an ERC20 token. Therefore it needs a parent Ethereum wallet to cover for transaction fees.
With $10 worth of Ethereum, you're able to do a couple transactions. Since the price of 1 Ether (ETH) changes almost daily, it's impossible to list the recommended amount in ETH. You can use an online USD to Ethereum Converter to find out how much $10 is worth in ETH.