Actually the best way to keep bitcoin for long time (for security reason) is cold wallet, that way you should write your private key on paper (if you want)
, and electrum can generate many addresses for you. first create standard wallet then create a new seed. menu>addresses
You seem to be a little confused about how wallets work.
Writing down a private key on a piece of paper is a perfectly reasonable way of creating a cold wallet for long term storage. However, you can't then use Electrum to generate "many addresses" from that wallet. A private key only creates a single address. It is a seed phrase which is used to create many addresses. If you want to back up an entire Electrum wallet or turn an entire Electrum wallet in to a paper wallet, then write down the seed phrase, not individual private keys. If you just want to back up a single address or create a paper wallet of a single address, then write down the associated private key.
Although "classic" paper wallets are a single private key backing up a single address, I would argue that writing down a seed phrase is better for a number of reasons - less prone to errors, don't need to sweep the entire wallet when you spend, no concerns regarding lost change.