At my company projects always start with P1 - research, and P2 - plumbing which are exactly what they sound like. The idea being to uncover and confront risk/unknowns as early as possible before some massive misguided investment has been made.
Projects vary at the low end from 2 people, 2 months up to 5-7 people for a year or longer. We do smaller stuff like prototypes also, usually as a first step in a longer series of releases. We are local in SF and frequently work in client offices. Budgets are between $100K - $1M.