
Most trades are licensed through a state governmental agency such as a "home improvement commission". You'll need to find the agency in your state and verify that the tradesmen is, in fact, licensed and in good standing.
Synthetic stucco is an elastic polymer installed over extruded foam insulation manufaturers include STO, Parex, Bonsal, El Ray, Dryvit, Master Wall, and LaHabra. Traditional stucco is a three coat process (scratch coat, brown coat and finish coat) using a portland cement based product.
Stucco is a somewhat colloquial term for portland cement based plaster. EIFS stands for exterior insulation and finish system, which is sometimes (incorrectly) called "synthetic" stucco. To complicate matters, "plastering" is the verb that describes the action of applying any of these various materials to a wall surface.
Looking at old stucco projects will tell you how the contractors work holds up over time. It takes several year for cracks to appear in stucco.
Depending on thickness of material, type of system and difficulty of the work expect to pay $7 - $13 per square foot.