I’ve had problems storing my stuff.
I ended up putting them in the bottom of the box my male clothes were in.
A pillow case may work
If not just wear them under your male clothes on the day of the move
As for the hair, I’ve had 2 wigs, both cheap off eBay.
The first one I ‘trimmed (if u could call it that)
It lasted me about 7 months, used 2-5 times a week.
The second one I have is cheap one too,
This is only because I’m growing my hair now,.
As zee said, it will look better from your own head.
Hope this helps