I actually bought everything except the latest DLCs, mostly during Steam seasonal sales. Same for EU4, which I've never played. Lots of badges without actually playing any of them (except for the CK2 tutorial).
My goal is to get some momentum and confidence with CK2. Once I "get it" and know how to keep a kingdom going for a few generations, then I'd like to try to deliberately explore specific expansion pack content (e.g., focus on the horse lords). And then, after focusing on each expansion in turn, I can try branching out to the other Paradox games in my Steam library (EU, Hearts of Iron, Victoria, etc.) Lots of games, but I figure CK2 is as good a place to start as any...
Which country would you recommend as a starting point if I have all my DLC enabled (except perhaps Sunset Invasion), but don't want to encounter any of the more challenging aspects of the DLC (like the aforementioned horse lords)?
Traditionally, a rite of passage in CK2 was always an Irish minor in 1066 but in this day and age it's far from necessary, save perhaps that very first time you load up the game in lieu of the tutorial or if you're trying to follow along with Arumba's old Youtube tutorial series. Really you're better off with anything ducal tier that's Christian and feudal in 1066. It's pretty much impossible to mess up, especially if you happen to go with something inside of the HRE like Tuscany or Bohemia. Unlike Ireland, you'll additionally have some gold, troops, and a better shot at marrying for inheritances as well having that same isolation and protection.
Beyond that, an ideal second game would be one of the Iberian kings or Poland to learn the art of war (specifically holy war) and then from there I'd take what you've learned and apply it to another religion of choice (especially one built for rapid conquest). Nantes or Jorvik in 867 would be ideal to learn pagan (Old Gods) mechanics since they are uniquely feudal rather than tribal. Your best start for an Islamic (Sword of Islam) game would be the Tullunids in 867, since you have the mighty Mamluks at your disposal and your neighbors aren't a huge threat. Whatever you do though as a Muslim, do not land your relatives.
After you get the hang of one of the other religions, go back back to Christians and try to learn the inheritance game- the Rurikids (Russian minors) in 1066 or one of the Karling realms (the Francias and Aquitaine) in 867 would be advisable. Afterwards put everything you've learned about war, vassal management, and inheritances and see if you can test yourself by starting off as a mere Christian feudal count. If you can handle that, then you're ready to try anything else you like- republics, tribals, nomads or the other religions.
On a side note, there's also no need to actually disable Sunset Invasion DLC itself- when you a start a game you can disable the Aztec invasion or change their spawn date with the recently added game rules. As others have mentioned however, it wouldn't be particularly ideal to have to deal with a huge army of angry Aztecs at your doorstep (assuming Western Europe). Another game rule to look at is Defensive Pacts, since they are meant to slow your expansion and can lead to very large alliance blocs that you won't be prepared for at all as a new player.