You are dealing with two different issues, the flat and appropriate pressure. As for the first question, the flat was likely caused by the rim tape problem, so get new tape, as has already been suggested.

Second, there is no one "correct" pressure. For a start, look on the tire sidewall for the manufacturer's recommended maximum pressure. (Sometimes there will be a minimum and a maximum.) But tire pressure is affected by the kind of riding you do, your weight, a choice between comfort and rolling resistance. Consider experimenting--a little higher, a little lower (being careful not to underinflate too much and risk pinch flats). Sheldon Brown offers this: http://www.sheldonbrown.com/tires.html#pressure, then scroll down to the section entitled "Pressure Recommendations."

Incidentally, you are likely to find answers to most of your cycling questions on Mr. Brown's site.