Hot wallet: The private key is kept online, though it can be a target for theft.
Cold wallet: The private key is written on a piece of paper, stored on a USB stick or even stored on a computer that doesn’t have access to the internet.
Hosted wallet: The private key is held by a third party service such as Coinbase Custody.
Banks: Some banks, especially online banks such as Bitwala, allow you to buy and sell cryptocurrency from a new bank account. They can also store wallets and private keys on behalf of clients.
The route you take is completely up to you. Some people prefer to keep their wallet information on paper in a safe, some prefer using third party services online and some keep it on hardware such as a BitBox (for Bitcoin).
One of the most significant factors to consider when leaving cryptocurrency in your will is the volatile changes in value. For example, in May 2013 the value of Bitcoin was around the £135 mark, but this year Bitcoin reached over £45,000 and then fell to around £23,000 due to announcements from Tesla and Coinbase.