FYI, you can buy a Mexican chip for your Belizean phone at the TelCel stand right as you enter the mall at CHEDRAUI. Its 140 pesos which right now is around $10 U.S. and comes with 100 pesos credit on it. It is very handy to have a Mexican chip for your phone when traveling.
Yes you need a club membership. It is around $40 U.S. for 1-2 people, if you already have a valid Sam's Club card from anywhere else in the world they will honor it. Probably the membership price is lower since the dollar is so strong in Mexico right now.