Your guy is quoting extremely cheap for those two replacements. Like unrealistically low.
Did you have your timing belt done yet?
You can do a leakdown test to see if coolant is leaking internally - but you should be seeing white smoke. If it's leaking externally check for drops under your car. A common symptom of headgasket failure is overheating when you're on the highway, and then temps coming down when you're coming to a stop.