Without going into a detailed explanation of JPEG, it is (in general) a lossy format: if you save a file as JPEG and then load it again, some of the pixels will have changed. However, unless you know what to look for you may not notice the changes. Moreover, there is flexibility as to how much information is thrown away: the more you lose, the smaller the file, but the more likely that the differences will be noticeable.

Your Nikon D3300 has three levels of JPEG quality (= compression): basic, medium, and fine. I suspect that if you adjust it to use basic JPEG then the result will be files of about 2-3MB instead of 12-15MB. (This is off the top of my head, based on what I observe on my D5300, which has the same sensor size).

However, dedicated image processing software has many more levels. It's not unusual for software to offer 100 different levels of compression (= quality). If you use the GIMP then when you save as JPEG you can adjust a quality slider and view in real time the results of the compression and the size of the file it will produce.

What I do personally is to save everything in RAW + Basic JPEG; I use the JPEGs as full-size "thumbnails" to decide which RAW files to process into high-quality JPEGs using Darktable. From memory, I think that I have Darktable configured to export at quality 98 of 100. Typically it produces files about 5MB, but the size obviously depends on how tightly I crop as well as the complexity of the scene. I would be surprised if Lightroom doesn't have a similar setting somewhere.

Factors to take into account:

• Whenever you load a JPEG, edit something, and save as JPEG you apply a cumulative lossy compression. There are certain changes to a JPEG which can be made without increasing the information loss, but they are limited to cropping at certain points in the image, flipping or rotating by multiples of 90 degrees, and certain colour transforms; and they require specialised software. Therefore if you only store compressed JPEGs you are effectively committing yourself to not making future edits.
• Whether it is "worth" storing a larger file depends on whether you have an SSD or a spinning rust drive (i.e. how much it costs per MB) and how many photos you take. I personally have taken on the order of 70000 photos in the past two years and am still a long way from filling my disk drive, so in my situation there's no real reason not to keep the RAW files as well as the processed JPEGs. If I get short on space then the first thing I can do is to delete the basic JPEGs, but for the time being that doesn't worry me.

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TL;DR

• You can get smaller files directly out of the camera by setting it to save in Basic or Medium quality JPEG.
• You can get better control of the quality/file size tradeoff using image editing software. Lightroom probably supports this.
• Which format to keep for long-term storage is a tradeoff: we can give you pros and cons, but the decision of which are more important is yours.