Vector files are the sharpest option as they never get "fuzzy" when enlarged.
Below two pictures.
The top a bitmap file which when enlarged will get "fuzzy edges" and below that a vector file which always stays sharp. Dont forget the brand is your advertisment and the promotional product is the carier. Your brand MUSt be properly reproduced.

Watch the word PLUMBING in the pictures below when this is enlarged.







Source of the information is from APPA. 
The Australation Promotional Products Association.
This information is part of a power point presentation given by the APPA CEO William Kestin.
Some parts have been slightly adapted to suit New Zealand conditions.
All material Copyright 2006 William Kestin.