No one else can answer this question for you. You have to look at the size of the photos on your hard-disk and see what the total size is and then buy a flash drive that is large enough to hold them. Larger flash drives are more expensive so there’s no need to get a huge one if things will fit on a smaller one.
Are you giving them your originals or are you going to work on them and give them saved JPGs after all your edits? What is the total size of 350 originals?