Methane is the simplest hydrocarbon. CH4.
One molecule of methane combines with two molecules of oxygen to form one molecule of carbon dioxide along with two molecules of water. Releasing good amounts of energy when this reaction (oxidation of hydrocarbons by simply burning them) is taking place.
CH4 + 2 O2 = CO2 + 2 H2O
Hydrogen is the simplest flammable gas. H2, in molecular form.
2 H2 + O2 = 2 H2O
Two molecules of hydrogen combine with one molecule of oxygen to form two molecules of water with no other byproducts. Lots of energy comes out too when hydrogen burns but it is a completely clean gas unlike any other. If hydrogen can be manufactured using only green energy, it is completely benign to the environment when burned. Also harmless when released unburnt as long as it doesn't cause any fires or asphyxiation or something.
OTOH when the methane burns it turns into an equal number of carbon molecules in the atmosphere in the form of CO2. Fortunately the CO2 has a lesser greenhouse effect than if the unburnt methane were directly released (or leaked) into the environment.
As it is now, any methane likely to be used as rocket fuel would alternatively just be turned into atmospheric CO2 by some other terrestrial user of natural gas anyway. Without launching any spacecraft.
Methane fuel still puts CO2 into the atmosphere at the push of a button, which would require a herculean effort to remove later, and that removal would not be justifiable until the situation is much more dire, as we have seen.
Still, methane really can be considered the cleanest burning hydrocarbon, but nowhere near the zero-CO2 exhaust from a hydrogen flame.
Both of these gaseous fuels are so light they do not like to be physically liquified at all, not even when highly pressurized, and that would require very heavy-walled storage cylinders in that case. But they still need to be stored as a liquid in order to carry orders of magnitude more fuel than the same size tank would hold in gaseous form. So they use extreme low-temperature cryogenics to liquefy these fuels and the storage & handling is accomplished at temperatures so far below zero that the product remains liquid without needing to be kept under very much pressure. Instead, it's handled very cold at all times with lots of insulation & refrigeration. If it warms up too much the pressure rise is certainly expected to exceed the design maxiumum of the storage tank, so all safety relief devices must be highly reliable under these conditions.
There's this thing about cryogenics.
Everything can't be expected to work right the first time, and success may not be had until all possible failures have already been witnessed to occur, and further design experience has been gained developing the workarounds.