First things first. If you're girlfriend has an iPhone now and is moving to android, be absolutely certain to turn off iMessage BEFORE switching from the iPhone. I would even do that days before to insure it is off and texts work as they should.
As for the switch to an S4 here's my thoughts regarding your questions. The most current software for the AT&T S4 is Jelly Bean 4.3, Kit Kat 4.4 has not been officially released yet. There are custom ROMs out based on 4.2 and 4.3 Jelly Bean that are debloated and based on Touchwiz, others that are based more on vanilla Android and yet others based on vanilla 4.4 Kit Kat. You could even turn it into a Google Play device with ROMs ported over from them. If you just want to go the rooting route, you could do that and install Titanium Backup to rid the device of any bloatware. Keep in mind doing any of these things voids your warranty and you run the usual risk associated with these changes. You can go to XDA and find plenty of ROMs for the S4.
If it were me I'd keep it stock, at least for a while. You can disable the bloatware and after that the only downside of having it on the phone is the physical space it takes up in the device storage. You would still have the benefit of the added features that Samsung brings to the device and you get to choose whether to use them or not.
If battery life is your motivation for considering these changes (rooting and custom ROMs) I can tell you that in my experience with the stock software battery life is very good. I'm currently running 4.3. After the update from 4.2 to 4.3 I did a factory data reset/restore immediately to make sure I had the cleanest install possible. I then reloaded my apps and set up my accounts. I have had no problems with the update. My typical day is off charger at 6 am and back on charger at 9 pm at which point I usually have at least 50% battery life left and many days I have near 70%. I'm not a heavy user but I do use my phone throughout the day. I have two email accounts (Gmail and Exchange) that I check and use all day, I text frequently, I rely heavily on Google Now, use my Google+ account, sync my Picasa account for images, Google Play syncs for music, I have GPS, Bluetooth and Wifi constantly on.
If you want to change up the user interface you can always add a launcher like Nova and theme it like an iPhone to make the interface more familiar to your girlfriend while she adjusts to android. In the end my advice to you is leave it stock and not root or ROM right after getting it, give it a while and if you still want to go that route do it later. The Kit Kat update is coming. If you root now you may not be able to get that OTA when it comes.
Good luck, hope she likes her new phone and hope this helps.