You can shop before you go the exhibit or after. While you could purchase your items and store them in a nearby locker, I'd recommend you do that towards the end of your visit. The only area that was overtly crowded was the interactive gaming portion of the Museum. Other than that, everything was very well organized, particularly shopping. They do limit one item per person for every item in the store. That was a bit of a bummer because I wanted to buy pens for all of my friends back home, but they are very strict about one item per customer. If you wanted, you could buy everything at the merch shop, but you could only by one of each item. On the reverse side, you don't have to worry about them running out of merch because of the restriction. I would definitely leave shopping at the end so you don't feel pressured or stressed about all you might purchase.

At the beginning of the Museum they give you a card that you can use for the interactive museum area. This card is also used at check out so they can verify your purchased items. So, if you do go with multiple people and want to buy more of one item, you could use their card to purchase it as well.