Sooo, i tested the orange sphere liquid fuel tank, and with only this and of course a small liquid fuel reactor to go with it, i was able to reach escape velocity.
My previous experimentations with orbits led me to consider a different trajectory than the obvious "go straight up", so this time i went straight up at slow speeds (under 500m/s) until i left the atmosphere (above 60km i believe), and then i accelerated to ~3000m/s but with a 45° pitch, then cut the engines with about half the fuel tank left, waited a bit until i was high enough, and then accelerated at 45° again for some time, until i reached ~6000m/s, and then again, waited, and i believe i was above 10 000 km when i repeated the maneuver a third time with the last of my fuel, which gave me almost 10 000m/s speed.
I also noticed a strange bug while i was up there : the higher you go, the more your actions generate Gs. I guess it has been incorrectly tied to the value of gravity or something. I was able to get above 30 000 G just spinning the rocket around
I also noticed that at some point the rocket just generates random Gs (up to 15G and above), i think this may be because the kerbian brothers move in the capsule and generate tiny movements, although it sounds weird. (the rocket itself had some sort of slow random spin over time, from a rest position).
As you can see my speed didnt go down much after the last thrust, it actually took about 30mins to go down from 9146.8 to 9146.7, and as long to reach 9146.6, so i think this is an escape velocity. I think what i did (the 45° thrust thing) is a form of slingshot trajectory, though i guess i could have optimized it by waiting a bit more after the first 45° thust, until i reached the apogee of my temporary orbit.
Edit : after a failed orbit attempt with a minimalistic rocket, i noticed that the atmosphere stops around 35km, not 60km. Could be useful.