What are the best cookies to ship?

Like everyone has noted: any drop cookies, unfrosted/glazed (this is especially important in warmer weather) preferably. It really comes down to how they are packed for shipment.

From my experience, I have found that rolled sugar cookies, shortbread-type cookies, and bar cookies also ship well. If they are packed snug but not tight, with little chance to move about in the shipping container.

I like self-sealing cellophane bags which helps to contain mess and breakage to one or 2 bags and not the entire shipment. I also like aluminum foil to packaging since it keeps cookies fresh longer and the wrapped cookies are cocooned so they don't shift around too much.

When I was stationed overseas- my favorite cookie box always contained crispy peanut butter cookies, Anzac biscuits, Speculaas and springerle. Since I wasn't a fan of anise, my grandmother would make them with orange oil or vanilla sugar, but traditional types would also make the trek well.

Gingerbread. The flavors actually get better with time. Shortbread.
Unfrosted or un glazed.
Oatmeal cookies. Most types of drop cookies...
I put my cookies into Ziplock bags & make sure to squish out as much of the air as possible.

Basically any classic cookie (i.e., 19th century or earlier) is going to work because they were created in an era without refrigeration.

Biscotti isn't a single cookie, it's really a generic Italian name for a family of cookies made similarly (twice baked, hence "biscotti"). Let's remember that Pliny the Elder wrote about baked goods using the twice-baked method (circa 110 CE). Every Italian region has their own biscotti (cantuccini in one popular Tuscan version) with different names and varying ingredients.

There are a bunch of good old Italian cookies that fall into this category, just look for "lunga conservazione" or "long conservation" in old cookbooks. Most of these old cookies don't have much in the way of fat (less to go rancid), especially butter.

With modern shipping speeds and generally cool weather in the Northern Hemisphere, I don't think it matters that much, as long as the cookie itself is durable enough to survive being tossed around by a common carrier (UPS, FedEx, USPS).

Think twice about shipping fragile cookies, ones with lots of butter (or fresh dairy), and deep fried items.

I will call out lebkuchen, the classic German gingerbread as a cookie suitable for shipping, again providing that any decorations are sturdy enough. The cookie itself can last months.

There are also classic cakes (English style fruitcakes, the Sienese panforte, etc.). Many of these date to the Middle Ages (or earlier).