You really don't need to overcomplicate things for this answer.
The key things worth knowing is that in an ideal gas (a good approximation for most at standard conditions (0°C and standard atmospheric pressure)) one mole of the gas will occupy 22.4 L of volume. A mixture of gases isn't any different and to know the weight of the gas you want you just need to multiply the molar mass of the gas with the proportion in the mixture (ppm is the proportion here).
So each ppm of methane will contribute about 16 / 1,000,000 g to each 22.4L of the gas mixture. Or (adjusting for the volume conversion to cubic metres which contain 1,000 L) 44.7 * 16 /1,000,000 g/cubic metre.
By this formula, a cubic metre of pure methane would weigh ~715g at STP so you could just work with that by multiplying by the ppm value.
It only gets more complicated if you need proportions by mass in the mixture: then you have to know the molar masses of all the other components. But, if you stick with volumes, gas laws keep things really simple.
PS if your conditions (pressure or temperature are different) the only thing you need to adjust is the volume an ideal gas under those conditions (molar volume is closer to 24.8 L at 25 °C, for example).