Unfortunately there isn't much you can do in your situation. The Zone 3 looks to be a budget phone with low end specs. It has 8GB of internal storage, and much of that is taken up by the OS. Apps themselves are getting bigger and bigger, so you won't be able to fit many on your phone to begin with. There are some things you could do, though.
Move your media and dedicated files to the SD card. The gallery app should have a move/copy function for the photos to get those to the SD card. Also make sure your camera is set to save to the SD card as well. You'll need a file Explorer to move music, documents, etc around.
Set up an automatic text deletion function through your texting app if possible. These do take up space and build up over time if you don't delete them.
This is a Verizon phone, right? They are well known for installing a lot of bloatware. Go into the phone settings > app manager and look for apps you don't recognize, especially games. Those are safe to uninstall. Some bloat can't be uninstalled, though. At best, you can only disable them.
While in the App Manager, look for one called DT Ignite. This is installed on a lot of phones and allows the carrier to install more bloat without your permission. If it's on yours, disable it. You may have to go into the menu and select to show system files for it to show up. You can't uninstall it, but you can disable it. This is the only system level app I'd tinker with unless your wanting to do a lot more research on what's what.
There is sometimes an option in the App Manager to move apps to the SD card. I would avoid this if possible. Not every app is programmed to allow this, they still leave some needed data on the internal storage, how much is moved will vary, and it can make the app unstable.
Some phones also had the option to mount the SD card as "adoptable storage." I've heard this has since been abandoned, but I'll cover it in case you have this option. Basically it treats the sd card the same as internal storage, theoretically giving you much more space for apps. The downside is this will format the card to your specific phone. You would no longer be able to use it in any other device unless you reformatted again. It would also mean if you removed it, it became defective, the phone could no longer read it, etc, you may not be able to use your phone at all. At the very least, you wouldn't be able to use the apps that are stored on it. SD cards are also slower to read and write to, so you could notice system slowdowns. This was generally ill advised to use.