I wonder if the +10% research speed is the best option from the get go to take as a first AP, some people say it's barely a bonus while some say it's very good. Same counts for taking Expansion, I always took Expansion first but basically once you reach the end you end up with Discovery as last one which is by then worthless as everything is already explored so I'm like coming back from that and tend to take Discovery first (3 times unity when finishing tech sounds pretty good too!). Also, no word still about the obviously very secret colonisation of 3 worlds already

?
It sure enables me to quickly fill the gaps.
I often take the 10%, but this time I was racing against time. Not long after I discovered *REDACTED*, which made the choice of target easy, but in any case I needed to take as many systems as possible.

In the south I already got a choke point, but in the north there are no less than two potential choke points I need to secure if possible.
As for the colonization... Well, I said I wouldn't cover every single event that happened, no?
I don't think there is a "better" one of the two - the reality is both Discovery and Expansion are very good, but their effectiveness decreases further into the game they are taken.
I mean, looking at Discovery:
Adoption: +20% Anomaly chance - only useful whilst still exploring
Science Division: +1 Research alternative - "nice" but hardly essential
To Boldly Go: Increased survey speed and disengagement chance - more useful earlier game
Databank Uplinks: allows assisted research - more useful later game when science ships have less to do
Polytechnic Education: Increased leader experience gain - useful throughout the game
Faith in Science: Unity gain with techs - useful throughout the game. Opportunity cost for taking it later
Completion: +10% Research speed - useful throughout the game. Oportunity cost for taking it later.
Then look at Expansion:
Adoption: +50% Colony development speed - more useful at beginning of game when energy is more precious and another colony is a greater proportion of your assets
Colonisation Fever: Extra unity for capital buildings - useful throughout game, opportunity cost for taking it later.
Reach for the Stars: -10% Starbase influence cost - Much more useful early game when actively expanding via building starbases. Becomes progressively less useful from mid-game
A New Life: +1 Pop on newly colonised worlds - More useful early game when the extra pop is more significant, but not bad throughout
Courier Network: -20% tradition cost from stations - useful throughout game, opportunity cost for taking it later.
Galactic Ambition: -20% starbase upkeep - useful throughout game, opportunity cost for taking it later.
Completion: +2 Core Sector systems - useful throughout game, opportunity cost for taking it later.
Unfortuately I don't think Stellaris has really slipped the leash that is the "bane" of all 4x games - going wide is almost always better than going tall. I mean, take my current EU4 game where I am Great Power #6 despite only having territory in and immediately adjoining the Low Countries. But development allows me to play tall very effectively, and synchronises well with Quality and whatnot. The beneifts of playing tall in Stellaris are more to do with comparatively smaller tech and unity costs - which is actually pretty similar to how tech used to work in the EU series prior to EU4, and whilst it does work "better" than in EU2, for exmaple, I am not sure it works well.