So I decided to restart the career mode once again, make a new flag, install KerbPaint, and instead of doing suborbital, orbital and then Mun's orbit, I've gone to Mun technically on the 1st flight.
The first rocket didn't even leave the launch pad, but was used as a rechargeable battery to transmit science gathered from around the launch pad:
That unlocked all required components to build my 1st flight worthy Mun rocket:
I didn't risk landing on the Mun on that first flight yet, because I needed fuel for powered landing on Kerbin, but instead only did a couple of rounds around it, lowering and raising the orbit to recharge capsules' batteries with the engine's generator (to transmit some of earlier gathered science), until the end of fuel in the penultimate stage, which I sent for lithobraking on the Mun.
(Sorry, no screenshots from that stage of the mission, but anyway, there was nothing interesting, just the Mun from 10K-500K altitude).
To leave some fuel required for powered landing I needed to deorbit and land on the dark side of the planet, or otherwise wait a few hours for the next orbit.
Thanks to the quick save I did before approaching Kerbin, I was able to return it without crashing in mountains (which I didn't see in darkness). The lander lost its parachute on the 1st try, because mountains made it opened much earlier than I expected, and I engaged the engine much too late.
After a few hours spent in darkness after the successful landing, Jeb and Bob left their capsules to check where they landed (at least they didn't land on a nearby tree
-- the mountains where I crashed on the 1st try are visible in background):
I think the amount of science gathered is not bad as for the 2nd mission in career mode (and I can use solar panels and batteries instead of engines and multiple capsules in the next flight):