If you want your beverage to be carbonated, that's another matter entirely. Don't use the juice bottles, but the plastic pop bottles work very well at holding pressure. If you use something that is not designed to hold pressure, like a wine bottle or a juice bottle or jug, you will have grenades when the pressure gets high enough. This won't work if you are already at the limits for the type of yeast you're using, however. None of these have to be aged in theory, though the quality improves a lot with age.
Carbonation takes about a week to two weeks.
It is usually best to wait at least a month on anything, and the longer you wait, the better it will be. Most references say wait at least six months or a year, especially for pure meads, but I've found things to be drinkable earlier. Keep the bottles in a cool place out of direct sunlight. Things age better if not jarred or disturbed as well. You can age things in the fermenting vessel as well, but bottle aging seems to work best for me.