I have traveled all over Mexico with different kits. PS, GF1, D300 with 3 different lenses. D300 with just my wife and/first child was fine. Once we had a second child the D300 was left behind. A PS just didn't give me what I wanted so the GF1 has been the camera of choice for the last three trips.
I know you said you didn't want multiple lenses, but my vote would be the GF1 and pick up a used 14-42 (14-45 may be better but it is 2x as much used) for $125. Grab a cheap waterproof bag for $30 and call it a day.
Don't overly worry about having anything stolen. Just use the same caution you would anywhere else and trust your gut. I recently figured that in the last 15 years I have spent about 11 months in total in Mexico. Not just tourist areas, but hop a bus and ride for 18 hours (with and without kids) to the middle of nowhere and not see another foreigner for days or weeks. The ONLY problem I have had is getting ripped off at the gas station. The attendants have all kinds of tricks to skim a bit of cash from you.
If you get a chance, take a trip to Merida. It is a wonderful city 4 hours west of Cancun. Make sure you hit a cenote or two. Start with Gran Cenote in Tulum and then try car wash cenote, Dos Ojos. If you have a car, you should also try to drive about four hours south to Bacalar and spend a night or two. The ruin of Coba is a must do as well.
If you don't do any of the above, then do just one thing. Rent a car or grab a bus and explore. You will find some of the most amazing people in the world there.
Darren