It sounds like you are ready to take control of your coins – thats a smart move.  Bitcoin Core is the original Bitcoin wallet. It is perfectly safe to use but, as with most other things when it comes to security, you have to take care of the security of your system. Despite some shortcomings, I believe it is still widely used. As for hardware wallets, they are definitely a safer solution because they eliminate the risk of an infected computer, but I personally would not recommend Ledger devices to anyone anymore because of their questionable moves recently. There are other hardware wallets that are a much better solution. For starters, look at those that have open source software so that anyone can check what they are doing behind the scenes.

With running your own node you can protect your privacy and help the network be more decentralized, but it’s not that you increase your security with running you own node.
Take note that any online device is always prone to hacking. If you want to be completely secure, you should generate and use your wallet on an air-gapped device or go for a good hardware wallet.

You are running a full node and you are asking about Bitcoin Core. I do not think you are telling the truth. Even if you are running an Electrum server or you are using wallet like Armory, you would have known what Bitcoin Core is before running a node.

Ledger Nano is not recommendable if you care about your privacy and if you do not want to share your seed phrase with another party. They will only give you a way to do that instead of them advising against something like it. The wallet secure element is close source.

For a hardware wallet, you can go for Passport. If you need multicoin wallet, you can go for Trezor.