maximizing battery life, at least for me is best with apps like Go Power Master or JuiceDefender. they have managed to maximize the life of my cheap little phone, just pick one and see which works best. stay away from task killers.
apps, the list can vary greatly. since you have 4.x you should be able to use Netflix and Pandora for video/music (of course GB users can too). another launcher is worth a try, there are many free versions in there that may give more custom features/themes without rooting. which brings up another part. do you want to root your device? the possibilities are endless if you want to root. you get all sorts of levels of customization doing that.
my favorite apps so far are
1. Go Launcher EX (w/ widgets)
2. Dolphin Browser HD (better than stock)
and many more.
Samsung Galaxy S4 **NEW** (GS3 screen finally shattered)
Samsung Galaxy Tab 3 7.0 (non-rooted, stock)
Samsung Galaxy Tab 2 10.1 (obsolete, slow, rooted)
Samsung Galaxy Note 10.1 2014 Edition