Choosing a new chain
This is the best test of chain wear I know of: it's in german, but the graph should speak for itself. His comment: "Chains were used under subjectively similar conditions - with exception of SRAM PC69 which, in nice conditions, lives for 1500-1800km"

Personally I think I rode unknown KMC, Shimano (probably HG-53), and afer having stumbled upon said findings, the Record C9. Different chains definitely have different lifetimes (and failure modes: some tend to tear, some lengthen quickly thus unusable). I have very good experience with C9, however, it is harder to mount (no missing link), and apparently it is incompatible with some slightly worn chainrings, but I'm not sure there. I posted a question on that problem here. IIRC, with me, Shimano chains wore fastest, KMC were somewhat better, maybe in the 2000-4000km range. The C9 lives some 10000 km for me. However, you seem to be located in the USA, apparently it's quite expensive there.

With cheap no-name chains I'd guess it depends on your luck. A bad quality chain will wear maybe in a couple 100km, and may tear.