I would like to embroider some wall hangings to send as gifts overseas, can you tell me the best material to use so they do not pucker.

I have used Heat N sta it is fusible tearaway with cotton & linen and it will prevent puckering.you iron it on your fabric, also hoop a stabilizer it works for me..

I've used bottom weight fabric and heavy twill for projects like this. Linen is too light weight in my opinion. Denim should be good, too.
MJDG

The puckering would be caused by several things - a heavy fabric would help - a wash away top & good cutaway back stabilizer could help eliminate puckers.