Roger, the older singer needles always had a rep for being top shelf, although the newer ones are generally considered less so than Schmetz, although for the most part, that's just urban legend and BS. They cost roughly the same however, and the Schmetz from my experience are available in much wider variety of sizes and styles everywhere I shop.
Especially when dealing with the lighter weight fabrics, I've had great results from the Schmetz microtex line, and haven't been able to find an equivalent version in Singer. In fact, of the readily available brands, I wouldn't recommend anything else for working with the ultra-tight weave 20d nylons (i.e. momentum). I've tried dozens of others and wasn't happy.
Size 60-70 in microtex sharp point.
For heavier weight fabrics it doesn't matter as much, but since the Schmetz needles run the same price or cheaper than the Singer brand, I stick with them.
I've heard good things about Organ brand being much cheaper and on par quality with Schmetz, however I've never seen them in shops.
So, I guess, I shouldn't have said no singer needles, just, merely a tip to branch out. Alot of skipped stitch problems that people believe are their machines having issues are actually one of two things a) in-appropriate needle for featherweight fabrics or b) wide throat-plate opening causing downward pucker and obstructing bobbin thread take-up (especially with zig-zag throat-plates).