Simple Bitcoin Wallet (aka SBW) is an open-source, non-custodial, autonomous wallet for Android. Besides basic wallet functions it has a number of advanced features such as Message Signing, Multiwallets, Transaction Bumping and Canceling, and more. Check user manual for details.
The recommeded way, especially if you're going to manage substantial amounts of money, is to install an app directly from GitHub APK file.
By installing it this way you make sure that wallet will never be updated automatically and thus exclude a possibility of malicious automatic update which may come from attacker who got an access to developer accounts or even from developer himself.
SBW has proven to be able to work reliably for years without updates and maintenance so historically this is the safest option to use it.