Bolo's tire pressure chart works very well, even though it provides PSI levels for riders who weigh 100 pounds to 150 pounds that are much lower than most lighter riders use. A 100 pound rider might be riding at 80 PSI on the same tire that a 250 pound rider uses at 120 PSI.
The PSI stamped on the tire is a MAXIMUM, based on a hypothical "average" rider and a hypothetical "average" rim. In real life, most riders will get the best performance from a tire at something far below the maximum PSI. But, a 250 pound rider will generally need to ride at, or even above, the maximum PSI to prevent the tire sagging beyond the ideal 15% deflection.
The chart is designed to provide a PSI that yields 15% deflection of the sidewalls under the weight of the rider. At 15% deflection, a tire provides the best balance between shock absorption, cornering ability, braking ability, and rolling resistance.
A puncture to the inside of the tube can be caused by the end of a spoke, or by a burr or sharp edge inside the rim. Find that defect, fix it, and then put in some fresh Velox tape. Using high quality inner tubes reduces the number of flats. I've had much better success with Continental tubes than with the "bargain" brands.