#69 thread is about tex 70. Different measurement systems, so it's just coincidence the numbers are close. A home machine may or may not sew these well. Many will, some won't. you'd have to try on your machine, and see. For your purposes, I think either of the threads you mention would work. Buy some of both, and see which you like better. It's important to match thread to the needle size. If you're using a big needle, you generally need a larger thread. Different thread diameters may require some tension adjustment. The gutermnan Jerry is using is probably mara 100. That's what's on the little spools of 'sew all' at fabric stores. It's usually much cheaper to buy it from someone who calls it mara 100, and sells it on 1000 or 5000 M spools or cone; one downside is that the color numbers don't match from the two sales channels.
As an aside, thread measuring systems aren't measuring diameter. They all measure linear density -- the amount a given length of thread weighs, or in older system, the length of a given weight of thread. Tex is nominally the number of grams a kilometer of thread weighs, but that's just nominally. There are only certain tex numbers defined in the standard, and there's rounding. The linear density is because it's heard to measure the diameter of something small and squishy, and because even on good modern threads, there's pretty substantial variations in diameter. Variations of 10 or 15% in spun threads are usual, less in extruded threads.