No matter when you decide to store your coins, it's known as a wallet and there are various sorts of wallets, for various requirements. It's up to you. I've been using crypto.com since they have launched. Didn't have any issues with them so far when it comes to deposits/withdrawals. I have Coinbase as well. Take a glance at these quite amazing wallet...
MetaMask
Trust wallet
Coinbase wallet
TronLink Pro
Crypto.com
I would urge to get a hardware wallet Nano Ledger, Trezor good value for money. You won't lose your crypto, best safest option.