Skans,
Nice to encounter someone else who is excited by low serial numbers. Regarding your questions, let me answer as best I can from the standpoint of my own collecting philosophy:
1) What do you consider a low serial number? Generally I consider a low serial number (low enough to warrant serious collecting excitement and a significant price premium) to be a number in the lowest 1/10th of 1% of the total production for that model. A couple quick examples from manufacturers/models that I am familiar with: For the Colt 1908 vest pocket .25ACP, this would mean a serial number roughly under 400. For the FN 1905 vest pocket .25ACP, this would mean a serial roughly under 1000. For the Mauser 1910 .25ACP pocket model, this would mean a serial roughly under 350.
Of course, my "1/10th of 1%" rule of thumb is very flexible depending on a variety of factors. For example, even though the total production numbers of the Colt 1908 .25ACP and the Mauser 1910 are not all that different (about 410,000 vs. about 350,000 allowing for the known gaps in the Mauser serials), the scarcity of low serial numbered guns for these two models - at least in the USA - is much more different that might be inferred from the production numbers alone. I have noted a fair number of the Colts with serial numbers less than 400, while any Mauser 1910s with 3-digit or lower serial numbers (let alone lower than the 350 threshold calculated using my little rule) are very rare.
Also, there is of course a large difference in scarcity and desirability when you get down into the really low ranges - assuming a given model's serial range began at 1 and ascended sequentially, it can be assumed that there were only ever 9 single-digit guns, then 90 2-digit guns, then 900 3-digit guns. And in most cases not all will have survived.
2) Do serial numbers only matter to you on 1st generations of a particular gun? Not really sure what you mean by "generation" - most of the guns I am interested in were a particular model that perhaps underwent several variations, but I consider a major model update to be a different gun with its own serial range, even if it took over where the previous model left off. For example, the Mauser WTP .25ACP model had a major update after the first 52,000 or so were made, with the 2nd model serials jumping a small gap and beginning at about 55,000 from the closest estimates based on surviving examples. I would therefore consider a WTP 2nd model with a serial number in the 55,000 range to be quite early.
3) How do you decide what kind of premium to pay for a serial number - go by gut? Research? Some other method? Combination of condition, exactly how low the serial number is, what model of gun it is and how rare. And yes, "gut" plays a big part.
