I'm a worldbuilder first and a conlanger second, so all the conlangs I'm working on play some role in the setting I'm creating and running a roleplaying campaign in. So I have (at least some amount of) culture and history to draw on as a starting point before I sit down to start working out words at all.
The name "Surkavran" itself was derived from (lit.) "language of the west"; Surek -- for west -- + -avran -- from 'papave', to speak --> 'papavor', that which is spoken (language) --> papavoran (contracted to papavran, and then -avran as a suffix), language of.
The earliest vocabulary I had was focused around geography, but that was more for practical reasons than anything... I was writing up a map of the region, and I wanted to label it in Surkavran, so I needed words for cardinal directions, "nation of", "map", etc.
After that was worked out, the next set of vocab I added to my lexicon -- which I feel like answers your actual question a bit better -- focused much more on the values of the culture itself. The earliest lexicon had adjectives like honourable, glorious, respectful, difficult/challenging, and traditional, and verbs like recount, attend to, know, allow, and be(come) part of. Sounds a bit stereotypical, I know, but the culture is actually a lot more multifaceted than that set of vocab would suggest at first glance... they are fairly core ideas, though, and so served as a good starting point.
The other language I'm working on, Ashgandusin, is a rather strange construction... it's almost more like a programming language than a natlang, and intentionally so. It's intended to be the language of creation, invented by the Elder Gods. It's equal parts language and magic system: concepts become reality simply by speaking them in Ashgandusin. ("Let there be light.")
The Elder Gods still do speak Ashgandusin, but the most common speakers by far (and realistically the only ones that mortals have a hope in hell of meeting) are demons and other nasties. So the language kind of evolved from that perspective -- acts of destruction, possession, etc are fairly straightforward to express. (As an example, "the fires will end once all is destroyed" is only 3 words, the fewest possible given the grammatical construction in place).
As another kind of cool note for Ashgandusin, root words are often concepts we would consider abstract, confusing, or difficult to put into words precisely (concepts in planar dynamics, cosmic law, etc), while relatively mundane/normal things ("that table", say) are much more complicated to express. Relatedly, "things" are seen as temporary manifestations of timeless entities... salapar is the root word for the eternal/undying concept of fire, but for a specific fire/flame, you'd prefix with mi- (manifestation of).