Can someone please give me a list of apps that are safe to uninstall or disable on my Galaxy S4? Thanks!
As stated it may not be possible to build a complete list, due to carrier bloatware. You may need some of these for functioinality you need also. There is also variants of the S4, to confuse matters further. This is not a complete list, but trying to keep one exactly up to date is like trying to build your house beside a boat, before you get the foundation poured the boat has moved on down the river.
XDA Bloatware List I must again emphasise that there can be roll on effects and you can lose functionality you MAY need on your device.
E.g.: AllSharePlay15.apk Removing will impact Wifi-Direct function. You CAN remove it, but you will lose WiDi and so on.
The alternative option is to find a Slim or Ultra-Slim ROM for your device. An example of this would be Echoe Illusion ROM for the S4 which has a SLIM and ULTRA SLIM variant of some of their ROMS. There is also the Google Edition 'Stock' ROM that you can use, which is 450 Mb approx, while Touchwiz Variant is about 1.6 Gb. There is also the Echoe Debloater which can remove bloatware from recovery, but the caveat of losing functionality still applies. There are many other ROMs out there too so shop around if this option appeals.
Note: Any mods/themes/firmeware must be for the EXACT variant of your device, such as GT-I9505, GT-I9505G, GT-I9500, GT-I9506 etc. Using the wrong ones can and most likely will brick your device.