Stellaris doesn't have a tech tree in the normal sense of the word, instead it presents the player with a quasi-random selection of technologies that may or may not appear later on during a playthrough.
A good analogy for this process is a deck of cards in which each card represents a different technology. As soon as a tech is selected for research, the remaining "cards" are placed back into the deck which is then reshuffled. However, in this "shuffling" some cards are weighted to appear more often than others. This is especially common in the early game where some "cards" are extremely likely to appear as to allow all players to get a fair start. Additionally, an empires' ethos, the leading scientists' traits, the current researched technologies, etc. all factor in into this weighting.
Certain technologies are considered "special" and are marked in a different color so players can to recognize their rarity. These are techs that might only appear once in a playthrough and, as such, should probably always be picked.
After some time it's possible to reach a point where procedurally generated techs get a chance of appearing more and more often after many of the "normal" technologies are successfully researched.
There's also the possibility of having "advanced" techs appearing during the later stages of a game. These are high reward/high risk opportunities that can give an empire a significant advantage in the race to victory but may trigger terrible consequences such as crises.
Technology is divided into three types: Physics, Society and Engineering.
As a game progresses, the technology choices for each empire will begin to include progressively more advanced and correspondingly more expensive technologies, meaning that building research labs and stations should be a priority. Technology costs also scale with the size of an empire's population, which makes it possible for small empires to maintain technological parity with larger ones.
The Betharian minerals appear to have originated from singular source, but were scattered across the galaxy millennia ago. The minerals are most often encountered as pebble-sized clusters, and are highly flammable.