From a copyright perspective, "commercial use" includes any distribution of copyrighted content to the public, whether it's intended to be used by end users in a public setting, at Church, or in the home, and whether it's distributed for free or for money. Distributing an app on Google Play or another app store would require copyright approval from the creators of any content you include.
There are only a few public music apps I'm aware of that target Latter-day Saints, and have a large selection of songs. One of them is LDS Music, which is produced by the Church, so is able to include anything that the Church owns or has licensed for publishing on LDS.org. Other apps have either not paid attention to copyright (not a good idea) or have used workarounds: Include only a subset of songs (the ones that are public domain and/or owned by the Church), work out their own license agreements with copyright holders for individual songs, or pull content from licensed sources (like LDS.org) on the fly.
Based on what I can see, there are three things in your app you'll need to consider when it comes to copyright:
1) Audio recordings.
2) Images.
3) Song lyrics.
Audio recordings
If you want to include audio recordings from LDS.org in your app, you can use them without permission from copyright holders IF you stream them from their source (LDS.org) or if you download them from their source (LDS.org) on the fly after the user opens your app. Copyright holders have already given permission to the Church to provide songs on LDS.org for streaming and download, so from a legal perspective, this is the same as a user following a link to access content from LDS.org. Where you will run into legal trouble is if you host the files on your own server, or bundle them with the app. Those uses would require copyright approval. You will want to give credit for the source of the recordings in a legal/about section of the app, and also mention that you are linking to the files rather than hosting them yourself, to be safe.
Images
What's the source of the images? Are they all from recent Church magazines or LDS.org? If so, you may be able to get copyright approval from the Church to use them freely. However, if they're pulled from Google Images or another source, each image likely has a different creator or copyright holder. A workaround, similar to the audio files, is to link to the images (in HTML, using the <img> tag to point to a remote image is legally considered the same as linking). Like audio files, you will not be able to host the images on your own server or bundle them with the app. I would also make sure you mention the source of each image. Include a link not only to the image, but to the image creator or owner's page if possible, and make it easy to get to. This may not be legally required, but is a gesture of consideration that will be appreciated by the image owner. Like the audio files, mention that they are being linked to and not hosted or bundled.
Song lyrics
This is probably the most important copyrighted material in your app, but also the trickiest to deal with, because there aren't good resources you can link to, to pull lyrics line-by-line into the app. You will probably need to bundle the lyrics with the app, or host them on your own server, in which case, you will need to either 1) only include a subset of songs, or 2) seek copyright permission from multiple copyright holders. Public domain song texts (as of today, anything published before 1923) do not need any permissions. Songs copyrighted by the Church can be requested for use via Permissions.LDS.org. For any other songs, you'll need to look at the copyright statement on the sheet music and try to contact the copyright holders. Keep track of anything you get approval for, and be sure to credit everything. The Church's legal department (via Permissions.LDS.org) may be able to help you find contact information for the owners of some of the songs (though they may not be able to respond to a blanket request for a large number of songs at once).
Hopefully this helps! I have a website focused on Church music, so I've navigated several of these issues myself.
Samuel Bradshaw • If you desire to serve God, you are called to the work.