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Man, a whole lot of arguing over semantics, and (surprise, surprise) you guys are both right in your own ways. Especially in the realm of exhaust, an entire lexicon could be written, including a full thesaurus. But, at the end of the day, all this arguing does the OP no good.
First, I don't recall what car this exhaust came on, but the basic rule is: Naturally aspirated engines need *some* back pressure in order to function at optimal levels. The size of the piping will be determined by the amount of exhaust the engine can put out. Anything larger than a 1.5 - 2 inch exhaust on a small N/A will probably have a detrimental affect on performance (including mileage).
Turbocharged engines are a little different in that they already have built in back pressure from the turbocharger. Theoretically, the more you reduce back pressure after the turbocharger, the more efficient the turbocharger will be. That's why some small displacement turbocharged engines will have 3" or greater exhaust.
My recommendation is, continue driving with the car until you can find a cheap (probably used) OEM replacement for the exhaust. Leave the headers (it is not worth finding an OEM manifold), and the OEM exhaust should bolt directly up. If not, it might need a slight alteration, but that shouldn't be much. This way, you have the normal back pressure from the cat and muffler.
A couple of words of warning, though: Tubular headers can cause an increase in exhaust gas temperature (EGT), and if EGT gets too high, it can damage the cat. This is especially true in lean burning engines. Also, I wouldn't recommend putting an O2 bung/sensor in the header itself. Headers tend to take the brunt of the heat from exhaust, so any welding/modification could cause the headers to fail completely.
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