For those having a hardware wallet, this article won't be any useful since they've already chosen the most secure way possible.

It is proven that storing crypto in web wallets can lead to unexpected losses. Not only there's a risk of the site being hacked, also more people can take a look at what you do with your money.  After all, to support the primary idea of cryptocurrencies - decentralization,  multiple clients' coins and keys shouldn't be stored on one server. There are really a few online wallets and exchanges that will let you keep the private key. Let's go download a wallet then.

But I don't have spare 300GB on a hard drive...

Technology goes forward, thanks god. You don't have to download the whole blockchain to have a local wallet.

If my computer breaks, what do i do then?

All of the wallets listed below will ask you to write down a seedphrase or export and backup a private key.

Here's a list of seed based software wallets:

Bitcoin - Electrum Wallet Download Electrum

Litecoin - Electrum-LTC Download Electrum-LTC

Bitcoin Cash - Electron Cash Download Electron Cash

MultiWallet (ECR20 capable) - Exodus wallet Download Exodus wallet

Dogecoin - MultiDoge Download Multidoge wallet

While it is still a bit more user friendly to use online wallets like Coinbase, the level of privacy and security that offline wallets offer should be a reason to consider using them instead. They can never be shut down and will never ask for your personal data.