I send my packages via FedEx Ground and it takes between 5-7 business days (not counting weekends or holidays) to get there. You can easily estimate how long and how much it will cost if you use the fedex online system.
As far as packing juice boxes and the like, really think about that in advance. They are not stable and can leak or spill if tossed about--like the packages are with any company. If you are planning a grocery stop anyway, I'd wait to pick up the juice at that point in time.
We've packed the following items, depending on what time of the year we are going: hot cocoa packets, cereal (full size box or small boxes) pringles (they break-don't do it!), granola bars, milk & cereal bars, fruit snacks, rice cakes, oatmeal packets, tea bags, drink mix packets, spaghetti sauce, spaghetti, sugar cubes, gum & candy, lollipops and small water bottles. I also pack items in gallon size ziploc bags before I box them to make sure nothing can get leaked on (whether it is from your box or another box or the weather!) or messed up.
Tape it up really securely, wrapping all around the box in different directions, and use a smaller box if you have to or send 2 smaller, I did! On the outside I made sure to make the name of the hotel and address, plus phone number, along with my name and arrival date. The also like you to mark it "Hold For Guest". The package will likely be delivered to an offsite location & when you check in make sure to let them know that you FedEx'd a pkg there and could they find it & deliver it. I always bring a copy of the FedEx page showing when it was delivered & who signed for it.
Anyway, sorry to ramble, but I love sending a box ahead. Last month I even sent a box of all of our personal items (like shampoo, etc...) it was great not having to pack it all at the last minute!