Manded mission to Mars or elsewhere in our solar system

That means an active refrigeration system. Hydrogen has to be the coldest, so it becomes the basis of the cooling system. Forced through a series of microscopic diffusers, Hydrogen Atoms are very small, it expands, expelled through a nozzle and gets even colder, basically a computer chip that exhausts LH2 = liquid hydrogen
Refrigeration takes little power, just a steady flow through the system.

Boiling point
CO - 81K
CH4 - 111K
H2 - 20K
O2 - 90K
Liquid Density @ Boiling point
CO - 788 g/L
CH4 - 422 g/L
H2 - 71 g/L
O2 - 1141 g/L

I suspect the change to solid boosters was political and military rather than because of performance after lift off. The main disadvantage of liquid hydrogen is 20 degrees k = 36 degrees rankine which is the familiar fahrenheit scale shifted to a zero of absolute zero. I presume the boiling point is a few degrees colder in vacuum, and only a few degrees warmer even under high pressure. Problem two is the density of liquid hydrogen is 0.5, lower than any other liquid or solid, so the energy is lower than some other fuels by volume. even though it is the front runner by weight. Volume does increase air resistance in Earth's atmosphere, but is almost irrelevant in the very thin atmosphere of Mars. The third problem with hydrogen is: it leaks rapidly though openings that produce negligible loss of all other fuels. We could reach Mars and discover we lost most of the hydrogen enroute, inspite of rigorous precautions. Hydrogen is not toxic to humans, except as it dilutes the available oxygen. Methane CH4 produces symptoms at about 1% and carbon monoxide CO at about one ppm (part per million) Both are deadly at high concentrations and the fire hazard is about the same for all 3. The tank to hold the hydrogen is less than twice as heavy as the tank to hold other propellents, and the oxygen. Thermal insulation is not very heavy, but it does increase air resistance, and it can damage shuttle tiles (and other delicate structures) if some insulation breaks off.
On Mars 1000 square meters = 10,000 square feet of photovoltaic panels would take years to electroloize water to enough hydrogen and oxygen to return to Earth: Forever with typical hydrogen leakage losses. Problems are the best electrolysis equipment converts about half of the electricity input to low grade heat and the electolizers have almost as much mass as the 1000 square meters of photovoltaic panels. It likely is not practical to fabricate anything for the first return trip from Mars on Mars, and not much even in a permanent Mars colony.
Can the return to Earth craft lift off with gas hydrogen under pressure instead of liquid hydrogen? maybe if the hydrogen tanks are made from CNT = carbon nano tubes which may soon be available, with a slight chance that the huge tanks could be fabricated from Martian carbon. Neil