As someone who has had BTC since it was $0.50 a coin. Ill give you my advice.
First you dont open a wallet, it is not a bank. You use wallet software or hardware to join the block chain. You can then generate a key which becomes your wallet. If you use a web site, then it is the web sites BTC because you dont own the keys.
If you can, set up a bitcoin core node.
https://github.com/bitcoin/bitcoin
The problem is that it will take a while to sync the whole chain which is around 669Gb in size. In my opinion this is the best way if you want to buy and store your coins for long periods of time.
You can buy a hardware wallet, IMO this is another secure way to store your BTC. For example
The Trezor 5
https://trezor.io/trezor-safe-5?utm_source=google&utm_medium=*****c&utm_campaign=SEA%20%7C%20Generic&utm_id=20546435881&gad_source=1
Just make sure you order it from the company and dont order it off some place like ebay or a dark web site. They have a hardware key and if someone else knows the key they can steal your coins.
Once you have your software or hardware set up you can create a receive address with it that looks something like this
bc1qenzys2n2cqx30pfuryszm7da2ykcnlwm3xmhsfbc1qpzbc1qpzhtkm87jyt34gg433ag54dfh2zkjudtd76m4zhtkm87jyt34gg433ag54dfh2zkjudtd76m4z
That is a wallet address and you can create a new wallet address to receive BTC to anytime you want.