Now you've come across the biggest myth in diving, "Your gear isn't good enough". It's a common approach by dive shops to get you to step up to the plate to spend 4 or 5 hundred bucks for their stuff instead of 40 bucks for the Wal-mart and Costco stuff. Now, the LDS has a point also. The quality of the packaged snorkling sets isn't very good, and your experience would certainly be enhanced by having quality gear, much like the difference between dirt bike riding on a Honda built for the job or one of those fat wheeled scooters powered by a briggs and stratton we all had as kids. Additionally, some LDS's require that you buy basic gear from them before taking a class. That way the instrustor can get to the business of teaching you to dive instead of figuring out how the buckles and snaps work.
Here is my suggestion. Try your Costco set for one lesson. Ask the dive shop to use a rental mask for another pool session. I think you will find that the mask from the dive shop fits better, is more comfortable, easier to clear, and easier to defog than the mask from Costco. YMMV, of course. One other solution is to look for used gear here and elsewhere. Lots of folks get out of diving and they have good quality gear to sell.