The main thing is to choose a good wallet, and there will be no problems with security and anonymity
A good wallet will keep your coins secure, but there is a lot more to staying anonymous than simply picking a good wallet. While the correct wallet is necessary to stay anonymous, it is not the only factor. If you use a web wallet you will never be anonymous. If you run your own full node you could potentially be anonymous, but not without taking further steps and precautions.
Which wallet are you using?
A variety of wallets, holding different amounts of coins, some of which I access daily, and some of which I haven't accessed in several years.
I have been using CoinsBank for 3 years, and there has been no reason to regret my choice so far
CoinsBank is a custodial web wallet, meaning they hold all your private keys, can watch all your addresses, and can see all your transaction. It is neither secure nor private.