I do not recommend using web wallets, but if for some reason, you have no other alternatives and this is your only option, at least make sure it's a non-custodial one. Meaning it gives you access to your wallet seed/private keys. This way you will have full control over your wallet and you can recover it any time you want.
Blockchain.com is a non-custodial wallet and does not ask for kyc. They also have an open source app if you want to use it on your mobile.