Trust wallet is a good and trustworthy wallet. The name actually speaks well of the wallet. Trust wallet is very easy to use and not complicated as other cryptocurrency wallet. Trust wallet is also used by many traders to securely store their cryptocurrency assets.
you can only use that wallet as alternative to myether and metamask but if you can use both wallet you dont need to download or use trust wallet those 2 is enough.
And for the security of your funds OP you should own the privekey of your wallet so what ever happen to your phone or stolen you still have access to the wallet.