It really depends on the butcher. Some will put a whole lamb in a box, others will put half a lamb per box, some might just put it in a big bag.
I would say standard cut is leg in 2, shoulder in 2, breast as a slab, chops in packs of 3-4. But that’s just from my experience of butchers. You need to tell them exactly what you want, and if you don’t know, just ask them. We have customers who like their leg and shoulder whole, some who like them as steaks, some the joints cut in half, some like them cut in 3.
Renting a trailer will probably be hard work, you’d be better asking a farmer to take them for you, or using a haulage company.