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.