Hey guys, a noob member here, as I've learned, there are a few ways to store bitcoins: Software wallets, hardware wallets, Paper Wallets, and Web wallets.
I will answer my opinion from your quote, pick the desired wallet as you want.
Software wallet: If you choose noncustodial wallet software, means full control of your funds on your hands. But there is still a risk of getting hack by device hacking. A custodial wallet means the fund isn't fully under the control of you and hacking possibility more than a noncustodial wallet.
Hardware wallet: Fully secured, just need to make sure your wallet credentials like seeds are safe. Hardware wallets hide your private keys, so even your device is hacked, the hackers can't see the private key and can't spend the funds. Always need to sign transactions from the device. Make sure to backup your wallet seed and both (wallet and seed) stored in a secure place.
Paper wallet: I wouldn't agree to use the paper wallet to handle your funds anyway. There is a high risk during generating and importing your private keys especially phishing attempts. Also, there are a few issues during spending like change address which would lead to losing your funds.
Web wallets: Web wallets are really not a wallet. It's just an algorithm. Because there are not true funds, they store your bitcoin under control of them because it's a custodial wallet. When you make a withdrawal, they just send that funds from their hot/cold wallet. I won't recommend it to use to store your funds.
Exchange isn't really safe to store your funds unless you want to trade there. For me, storing your funds on a hardware wallet is quite safer than another wallet. If the amount is bigger then perhaps you would choose a cold wallet as well. Depends on you now which wallet suits you. Please always make sure the address when you are copy pasting.