In this paper, it is commented about "fresh" samples:
"....stainless steel samples at successive stages of sample conditioning: shortly after cleaning (fresh), after subsequent exposure to ambient air and after subsequent residence in the introduction chamber and analysis chamber of XPS spectrometers (duration given between brackets). Data given on a line refer to a set of experiments providing a sequence according to time and treatments."
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Article Organic adlayer on inorganic materials: XPS analysis selecti...
If by fresh you mean clean then unless your sample contains C then you can't use the C 1s. In reality it doesn't matter too much what you use for calibration (so long as it is a well defined and narrow peak) and you state precisely what you have calibrated to and the energy you have set it to. Obviously you should use a reference to a material as close to the one you are using as possible. As long as other researchers know how you have calibrated your spectra then it really doesn't matter too much what you use. Finally, for the best calibration, if you have a metallic sample, or a metal in direct contact with your sample, you can try to take a Fermi level spectrum, which has a binding energy of 0 eV by definition, although the cross section for photoionisation in this region is small for lab based X-ray sources.
Other folks here have got the calibration bit covered, so I'll just worry about the sample freshness part of the question.
One way to tell how "fresh" your sample is would be to compare it against pair of similar samples. One that you know is "fresh" and another that is definitely not "fresh" to see what to look for (oxygen peaks, metal oxide peaks, etc.). The real trick here is making sure your sample actually is fresh.
For pure elemental samples (gold, silver, iron, etc.) it's pretty straightforward. Prior to measuring, you can sputter the surface (typically with an argon ion gun) to clean it, removing any oxide or gunk that's contaminated the surface to expose a clean pure elemental surface.
For compounds (especially containing atoms of very different size, as sputtering will remove them at different rates, exposing a non-typical surface), modified surfaces, or films that sputtering might destroy, it's going to be trickier. My best advice would be to prepare your sample in a glovebox and use a transfer mechanism (sometimes called a "vacuum suitcase") to move it to the XPS, but not everyone will have one of those. If that's your case, by best advice is to prep your sample in a glovebox try and find some way to keep it from touching atmosphere/water. I've had some success with storing samples under degassed hexane or toluene and quickly mounting the samples under an inert gas flow (usually of the XPS's intro chamber) before putting them in the chamber. It's not perfect, but it will probably at lease be "more fresh" than just having it hang around in air.
I would just add to the calibration part of the question that specifying the BE values for some reference core level (C1s, Au4f, Ag3d or whatever) only makes full sense if it is also ensured on a regular basis that the spectrometer Fermi level (Fermi edge position of a metallic sample, preferably Au or Ag) is accurately mapped to zero BE. In combination, that assures accuracy of the voltage supply to the analyzer.
And yes, cross section for the latter is low, and it will cost time to obtain good data for that purpose. But if a good calibration is wanted, there's a price to pay...