Oxidation can be a problem OR a deliberate part of the taste profile. For example, sherry is a deliberately oxidised wine and tastes really nice. If your mead is sweet and high in alcohol it may actually benefit from oxidation but if it's a fresh, low alcohol type it will probably destroy it. If that makes sense.
use nice small beer bottles with crown seals. it's a good way to bottle aged mead even if you aren't running short.
edit: Keep it in the demijohn as long as you can. Someone told me that the conditioning process happens better on a larger scale. Maybe because of the amount of yeast?
How you store your mead is probably more important than the bottles you store it in.
edit2: got confused by the new question... mixed 'em up.