Depending on the length of the flight, a shower at the destination is best
However, for redeye and flights longer than 7 hours my basics are Olay face wash cloths (the foaming type) usually at the destination airport and rinse off with warm water. I do this on the plane if I'm not sure about the airport facilities. Plus, I have a travel toothbrush and toothpaste.
For longer flights, I use the single-use paper moisturizing masks plus have a small wash cloth with me.
I always have a few hair ties and tie my hair back to prevent it getting overly static.