Two barrows - excellent. I reckon the best way would be to leave them with me and I'll 'look after them'!
We used to leave them on the top of the ground to dry in the sun, or on racks in the shed until the tops were all shrivelled and the skins were that lovely healthy tan looking. Remove any that showed signs of fungal attack, and eat them/discard them. Then we'd hang them somewhere cool, dry, frost free.

see if you can get a string bag from the greengrocer or veg section at the supermarket. failing that I have seen them stored in the legs of old tights/stockings,

I agree with Worthy on this - lift and leave on the ground to dry off then either plait or put in an old pair of tights.