Still no smartphone here (same flip phone since 2005,) but recently got an Android tablet.
I rooted it and installed CyanogenMod ROM as well as TWRP recovery. They work pretty well, although I only used the stock system for a couple days and not sure what all is really different, but it's supposed to provide a lot more settings.
If you want to root easily, co-worker told me about WugFresh utility that makes it easy to make backup, then root or un-root device. I checked it out, but installed the Android SDK and did it from the command line just for better understanding of process.
As far as apps:
System - ES File Explorer, StickMount (for USB drives), Titanium Backup (haven't bought pro, free prompts every app), SD Maid
Media - DicePlayer (stream video from local server), VLC (stream music from Internet Shoutcast/Icecast servers), Foxit PDF (not sure if better app, I use it on PC)
Web - Dolphin browser (I try to avoid Google, it's alright but sometimes open tabs are gone. Can still open in history. Installed last version of Flash for Android straight from Adobe website to play embedded videos. Stock Chrome played embedded vids as well.)
Games - Hill Climb Racing, Stickman Downhill Racing are simple but addictive. I tried out a few games resembling Galaga, I need to try some outside the Google Play store to find like original. Yet to install console emulators and ROMs.
Not sure on spying outside of Google, but there's an AdBlocker app I saw and still need to install. Those racing games have in-app ads.