When you're exploring JPG vs. TIFF, there's no need to decide between one or the other. You can have both. Because the TIFF is capable of storing so much more data, this is the file you will want to start with. Once you have made your edits and done what you want to do to the photo, you can save it. Then, you can choose to save it again, only this time as a JPEG.
There are a few benefits to having two files of the same photo. The first is that you have a raw image with no data loss or compression. This will allow you to make all of the edits you want without losing anything in the process. Then, you can have a smaller version so that you get the edited photo without all of the extra file size behind it. The JPG is going to be a small percentage of the megabyte count of the TIFF, allowing you to share it in social media, email it, upload it to your website, and more.
You'll be able to keep track of what photos are in what format because of the file extension listed. You can even choose to separate the files even further by using folders. This way, you know which ones have been compressed and which ones haven't.
Additionally, there may be a few other file formats that you will want to create once you have a photo that you like. This includes PNG and GIF. Just like JPEG and TIFF, there are pros and cons for you to discover about them all. Just remember that the TIFF is going to be the largest photo file type, best for using photo editing software. Once you've made your edits, you can save in any file type you desire.