What is the proper way to prepare a solution aiming to minimize errors?
Methylene blue isn't a primary standard so I'm not sure how much accuracy/precision you need. 


Typically when wanting the best accuracy the solid would be dried in
a hot oven, then cooled in a desiccator.
Do not to handle the beaker with your hands. Even if it has been
"left out" in humid air that amount of water would be stable. So use
tongs to pull in and out of balance.
Another option is to weigh more and do a serial dilution. So 1 gram
in liter, then 10 ml of that solution into 1 liter.