Unless the greenhouse is heated, your "first faucet" has to be treated as if it's out of doors. That means you have to trench about a foot deeper than the frost line (call before you dig, and get utility locates) from the house to the greenhouse, and use a "yard hydrant" as the greenhouse faucet. These hydrants are like giant frost-free faucets, made to connect to deeply buried waterlines, for year-round outdoor service. At or near the point where the yard hydrant is connected, you can tee off to a line to feed the warm-weather faucets, using a "curb-stop" valve that opens and closes with the same sort of key a city water department uses. Some of these curb stops have a drain feature that will empty the downstream line when the curb stop is closed, assuming you keep the waterline pitched so as to allow this drainage. Both curb stop and yard hydrant have a bed of gravel around them, to allow for better drainage, as the yard hydrant also will self-drain when it is shut off.
The supply for this project will start in the basement, exiting below grade. You might need a backflow preventer in the supply, because of the below-grade drains in the outdoor valves. The kind of pipe used for the deep outdoor line would be specified as 160-psi-rated poly pipe, preferably the medium density version favored by submersible pump installers, which is a bit softer and more easily clamped to the brass insert fittings a project like this will employ.