Excuse me if I'm over-simplifying, but I don't know your background experience. Realize that system apps don't get "installed" in the normal sense. The .apk (and .odex, if there is one) get moved to /system/app or /system/priv-app. Next, the file permissions have to get set to 644. It's also a good idea to delete the dalvik cache (i.e., the contents of /data/dalvik-cache). Finally, reboot.
The first thing you'll see after the boot animation is a "Android is upgrading" message. This is the result of it seeing the new system app and building the Dalvik cache for it. If you deleted the cache entirely, it will take longer of course, since it has to rebuild potentially hundreds of file cache entries. It's all perfectly normal; just be patient. Assuming you don't have any missing .odex, library files, or symlinks needed for the program to run, everything should be good to go once the phone boots fully. Problems occur when you partially delete stuff or don't know what was deleted. I have backups of most of the AT&T bloatware from my old S4 (on Android 4.3), so if you can tell me specifically what you need or what is not working, I might be able to provide you the missing files. Failing that, your only solution is to start over by flashing a factory ROM (a factory data reset won't help).
Here are the app packages I have available (sorry, MMS isn't one of them):