Does a factory reset get rid of all of the customization I have done to the phone? I imagine that it would but I have never had to do one at this point so I am unfamiliar with what exactly is involved.
Yes, a factory data reset will restore the phone to a new out of the box state (software wise) and you will have to set it up again. If you are using the sync and backup options of your Google account and if you created or signed into a Samsung account and are using its backup options, much of your current setup will restore when you sign back into those accounts. But you will still have some settings to redo.
There is one other option you may consider trying before performing a full reset. You can wipe the cache partition. This will sometimes clear software issues. It does not delete any of your settings, stored data files or installed apps. It only takes a few moments to do and may be worth a try prior to a full reset. The procedure is - Power off your phone, then press and hold the Home, Volume up and Power buttons simultaneously (I usually press and hold the Home button, then the Volume up button and lastly the Power button - all must be continually held down), when your phone restarts and you see blue text appear in the upper left portion of the screen release all three buttons, your phone will boot into Recovery Mode, in a moment you will see a list of options in blue text in the upper left of the screen, scroll down the list using your volume button to navigate until "wipe cache partition" is highlighted, then press and release the Power button. It will only take a few seconds for the function to complete, when it is done you will see confirmation in green text in the lower left of the screen. You can then use your volume button to navigate to and highlight "reboot" and then press and release the Power button. Your phone will restart and you can test your wifi function to see if this cleared the issue.