New Schwinn 700c (bike in a box) assembly
As stated in comments grease the pedals and seat post to prevent them from seizing.  Quill stem you might grease.

The bearings should come lubricated.

Pretty much any grease (except computer).  Bicycle grease is more for bearings but you could use it. If you are going to buy some just get general purpose grease.  

Tip pedals are right and left.