Might be worth reading through https://bitcoin.org/en/secure-your-wallet.

Personally I use a local encrypted wallet (standard bitcoin core software) that I back up to USB. My assumption is that the strength of the wallet encryption is good enough that even if my PC or USB is compromised the wallet pass phrase will keep my coins safe.

I use an air-gapped solution. I can create unsigned transactions on my watch only wallet (Electrum for example), transfer to the completely offline machine, sign and return to the online machine to broadcast it. It is a long and laborious process. The watch only wallet is created by using the xpub key.

Take a look at iancoleman.github.io/bip39/ to learn a bit about BIP39/BIP44 HD wallets and how a seed phrase can generate all the addresses. You can use this in an offline computer to generate your own phrase, just like blockchain.info did for you. It will give you the xpub too for online watch only wallet, this is how to use in electrum: docs.electrum.org/en/latest/coldstorage.

The value in a hardware wallet, such as the Ledger, is that it allows you to be air-gapped without a second machine (or booting from read-only media). It's fast and secure.

You do need to keep that HD wallet BIP39 Mnemonic safe with any solution. I don't have any suggestions on that front.

Other answers have not touched yet on paper wallets.

A paper wallet is an offline (paper) wallet. Provided the wallet is created securely (offline) and the random seed is true random without flawed random logic, paper wallets are as secure as you can get. You only need to protect the private key on the physical paper wallet.

For Bitcoin and many other currencies, you can use a paper wallet generator such as walletgenerator.net following the instructions on the website (note, I cannot personally vouch for how truely random the generator is) and once sealed you send your BTC to the public address. Provided the private key is never revealed your coins are as safe as possible.

When you wish to spend from a paper wallet, it is necessary to import the private key into some software that can generate and sign a transaction for you, e.g. Bitcoin Core or Electrum. It is common practice to expend the paper wallet entirely for the truely conscientious security mind and send any change to a new paper wallet but it is necessary to be mindful of where change will be sent in either case.

What I basically want is to store my coins offline

I would extract the private key or recovery phrase from the account at blockchain.info. I don't know exactly how as I don't have an account there.

If that proved to be impossible I would create a normal wallet using something like Bitcoin core on a newly reformatted and installed PC. Then I'd send the bitcoins from the blockchain.info account to the receiving address of the new wallet (I'd test this first with a vary small amount). Then I'd extract the private key and put that PC offline.

I'd then practice using that private key in yet another clean PC to be sure I knew how to recover access to my bitcoins. Once happy I'd write that private key (or recovery phrase - whatever I'd practised using) on paper and lock it in a safe (and tell my next of kin where to find it if a bus knocks me down and kills me).

Then I'd delete the wallets created on PC's and at least zero the unallocated space.

but have a wallet where I can see exactly how many coins I can access with the offline stored code (without giving the code to an online wallet).

This is called a watch-only wallet. Or more accurately, a watch-only address in a wallet. I believe most, if not all, wallets can do this. You just import the receiving-address only (not the private-key or recovery-phrase) into the wallet.

Here's an example using the Electrum wallet