Simple Bitcoin Wallet (aka SBW) is an open-source, reproducible, non-custodial, autonomous wallet for Android. Besides basic wallet functions it has a number of advanced features such as Multiwallets, RBF, CPFP 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.
WalletScrutiny.com is a service which makes sure that a usable application which gets installed on your device is built exactly from its publicly verifable source code and does not contain any secretly added parts (which could be malicious or spying modules). SBW passes all WalletScrutiny tests and as such it is a proudly reproducible software.
Additionally, if you trust no one but yourself, here is an instruction on how to build a wallet APK file directly from its source code.