1. Bitcoin core and electrum are in fact host storage wallets, so it is kind of strange that people refer to them as the best wallets.
What do you mean by "host storage" wallets? With both Core and Electrum, you generate your own private keys and you are the only one who can access them. This is generally referred to as "self custody" or "non-custodial", to differentiate from web wallets or exchanges where a third party holds your private keys for you.
Both Core and Electrum can be used as a simple hot wallet on an online device, which is the least secure way to use them. Similarly, both can also be used as a cold wallet on a permanently airgapped device, which is a much more secure way to use them. And if you are using them on an airgapped machine, you can also use them to generate key pairs or seed phrases that you then print out or write down to create paper wallets.
2. I know that this is private, so feel free not to answer it, but when it comes to you, where do you store the keys to your coins? Do you have a combination of hot storage and cold storage?
Yes, exactly that. I have a small amount of "daily spending" bitcoin which I carry on a mobile wallet. Insecure, but very convenient, and only ever an amount I can easily afford to lose. The vast majority of my coins are in a variety of more secure wallets, including hardware wallets, airgapped cold storage, paper wallets, and some multi-sig wallets involving a combination of these things. All my wallets are synced from my own node to minimize any privacy leaks.
I meant hot wallets. OK so I totally understood how you can use them. In fact I used to own a Trezor wallet which I think also Connects to electrum.
1. Bitcoin core and electrum are in fact host storage wallets, so it is kind of strange that people refer to them as the best wallets.
Are you trying to say hot wallets or maybe software wallets? They are, yes. However, Electrum can be both a hot and cold wallet, meaning you can use it on an internet-connected computer or a permanently airgapped device. Bitcoin Core is a full-node client, which needs internet connection to update and sync the newest blocks. Electrum being a light client that doesn't require downloading the whole blockchain to work is easy to take offline. I think it's still doable with Bitcoin Core, and I could swear I saw an old guide for it in the past. But it's not user-friendly having a full client that is offline.
Yes, my confusion was that I thought those wallets could be used only as hot wallets. I knew they are software wallets but it never occurred to me that I could use them "offline"