Another important thing to remember, if you want the best resolution, is to save in Raw format, not as a .jpg file - that uses lossy compression - you lose resolution just by saving as .jpg.
You don't lose resolution with jpegs. What you lose is some of the fine details when it comes to dynamic range, effectiveness of noise reduction, and color saturation. This limits how effectively you can edit a photo (if you choose to).
RAW editing allows for absolute control over those details, because the individual pixels still have all the info from the sensor. One of the better known examples is the recovery of blown out highlights. With a blown out highlight in a jpeg, you get pure white due to the data compression. That same image in its RAW format could still have details, and turning down the highlights allow those details to remain visible. The downside to all this is RAW files are not viewable on most devices and you need a RAW editor to see them. You have to edit them because the sensor data is often dull, then save as a traditional image format(jpeg, png, tiff, etc).
You can find RAW editors for android. Snapseed can do it, and there's also Photoshop Express for free.
To the OP, just keep in mind that this has zero the do with original topic of cropping photos. It's good info to know in case you want to explore image editing, but isn't necessary to know for basic cropping. Depending on how deep into the weeds you want to get into, the choice of doing the edits on your phone or from a computer can get rather muddled. A crop on your phone and the same crop on the computer will look identical in the end.
If you do move on to editing image details, then you may want to consider things like monitor color calibration. Depending on the phone and monitors you have available, the phone may actually be more accurate than a monitor (a situation I'm in compared to my laptop). Color accuracy of the monitor determines how close the final print looks to what you wanted. If you have a red image on an accurate screen, it'll look just as red when printed. If the screen is out of calibration, what looks red on the screen could come out pink on the printer because you edit based on the screen image and not actual image data (unless you can read binary like Matrix code). There's ways to match your monitor to the printer to account for these differences, but I don't think you can do so on a phone.