Better strat:

Vult rush (effective against p, and t, not z because of mutas)

10 depot (always on islands...)
10 refinery
12 barracks (or if you get enough cash)
15 depot
scout with barracks
get 2 facts
get starport
tech mines, get dship

Not too descriptive, but you will develope a certain flow, i used to get comsat and scan before i dropped, very effective.