I like you generally start with infants and stay with a family through toddlerhood. One thing I generally request is my own diaper bag. I like having it stocked up with my own essentials (hand sanitizer, wipes, extra clothes, a snack for nanny, my lip gloss, my water bottle, etc...
Another thing I love to have is the ErgoBaby. I wear baby on most of our walks! I do love the BOB as well for trips where we need to carry more gear (like to the beach).
Last big piece of gear I love is the baby Bjorn bouncer! Best bouncer out there!
Random little things: a paci case to keep a spare paci clean if baby uses them.
A&A swaddlers, amazing, enough said...
Once they hit toddlerhood, there are more food and snack related containers that make travel easier too..