You’ve got the link to Bitcoin Core right at the top left of this page (where it says News).
Anyhow, If you can afford it, a hardware wallet is safe and easy to manage (i.e. no need to download and maintain over 200GB of data if you intend to run a full node just for your BTC (and only BTC) wallet).   

I believe in a cold wallet because it can be the complete offline wallet. When your wallet is offline, you no longer have to worry about any attack done by the hackers. Just remember that you need to protect and keep your crucial private sequence secure.

To make it easier for him, here's the link --> https://bitcoin.org/en/download

I don't think that it would be wise to encourage others to use it because other really good wallets like Electrum were made specifically to solve the needs users might have when using one and they are constantly working on improving it. You will encounter a lot less bugs and have a lot easier life using it.

Hardware wallets are second one in security but first in security/convenience balance. Cold wallet is hodler and you won't lose the piece of paper.

I personally use Electrum and our local wallet in securing and storing my holdings. I find electrum safer than any exchanges and wallets. Also, I trust our local wallet because it has been providing secured and good services for years.
Securing our holdings in a safer wallet is really necessary.

If you have good internet and a computer dedicated to store your wallet, you can use core wallet
You can use Electrum, it's a very good wallet, and reliable

In any case above, the only person responsible for your safety, is YOU

If you have a large amount of money, it's better to buy a hardware wallet

You're not exactly wrong. The reference client is a full Bitcoin wallet which downloads and verifies the entire blockchain. Given so, the wallet can be sure that they are on the blockchain for which the blocks and transactions follows the protocol rules. Hence, it does not need to trust anyone else to run,

With SPV clients like Electrum, they rely on another node to provide the information. With how Electrum works, it uses an ElectrumX server to get all the information and cross verify them with 8 other Bitcoin nodes. Whilst this is secure enough, Electrum is still susceptible to sybil attacks. Since the client does not validate all the blocks and transactions, it is possible (though very expensive) for a few malicious clients to fabricate information to scam you. For the average joe, this is unlikely as the client usually connects itself to diverse nodes and a single honest node could break the attack.

Bitcoin Core is a good choice, but it needs a lot of resources and maintenance. There is nothing wrong with having a mix between desktop wallets and web wallets and storing small amounts of coins on exchanges and using hardware wallets and paper wallets for long-term secure storage.

I find that several wallets distribute the risk of losing all your coins in one hack and that accessibility and convenience force you to use some implementations with weaker security. <You just make sure not to store large amounts of coins in services with weaker security.> 

It's one of the best wallet you could use but I have to agree with some of the users said above there are other wallets that are better and less heavy than core in some way like the hardware wallets. And if you don't want to spend money on a wallet there's other good desktop wallets too like Electrum, Wasabi, Armory, GreenAddress and many more.