Personally, I disagree with the generally accepted notion that Innovative is less desirable than Administrative or Religious/Humanist. I find Innovative more valuable and versatile than Administrative in most games. (I presume it's mostly because I like to play minors in Western and Central Europe, and have little interest in the tedious rebel management you get when doing a WC. But I can't imagine most players are doing WC after WC.)
Key things Innovative offers:
- -10% Tech cost
- Less war exhaustion, which translates to lower coring costs and not wasting diplo points to reduce war exhaustion
- -25% advisor cost, which allows to afford level 3+ advisors much earlier (and policies to double down on this)
- A regular stream of -10% tech cost events
- Several great policies (in particular the ones with Quality, Offensive, and Influence)
It's a good idea group that saves (or gains you) lots of monarch points in practice. My only issue with it is how it gets in the way of Court and Country. Unless you're reducing autonomy all over the place in a large empire you'll usually get Court and Country in the 2nd half of the 17th century. Having Innovative, Humanist, or Plutocratic by then - to say nothing about having all three - gets in the way of having +1 unrest.
Administrative, by contrast, basically invites a blobbing game with:
- -25% core reduction cost
- -10% admin tech cost
- 3 mercenary-related ideas of dubious use if you're aiming for 100% professionalism
- Mostly meh policies (only the ones with Influence and Aristocratic are worth it)
The only time I ever get Administrative is when I intend to core three or more of Europe, the Middle East, India, SE Asia, and China. And it's usually a mid- to late-game idea at that, because unless I start as a large country my early games are usually constrained by military might, siege speed, and AE more than by Admin points.
It might be specific to where and how I like to play, but I've lost count of the number of times I was nearly finished coring Italy, the Low Countries, or a large chunk of Germany without a hint of Admin point shortage by the time I got Administrative's Core Cost Reduction. The real blocker is the long list of countries with 80 AE opinion that you're scrambling to compensate with improved relationships, gifts, and influence nation.
Making matters worse, you subsequently find yourself swimming in so many Admin points that you're basically forced to blob all the way to China just to have something useful to spend those Admin points on. When you take it as Portugal, you'll invariably find yourself coring Maghreb and Egypt in full at some point because AE is so unfathomably high in Africa and Asia (and the diplomats are so slow to return) that you can't continue to warmonger in those regions without risking a worldwide coalition.
As to Religious and Humanist, I've only ever found them useful when painting the map.
IMHO, there are three cases:
- Map painting game as large nation: Get Administrative, and either Humanist or Religious (Russia, Ottomans).
- Map painting game as small nation: The same but Influence and a mil tech are more important in the early game, because AE reduction and military might will be more useful then.
- Casual SP game: None of those groups matter. Consider Innovative and/or Economics. Or for that matter, things like Trade or Espionage.
I've never tried playing MP but my understanding is that Economics and Innovative are solid picks there, alongside the Offensive/Defensive/Quality trinity.