Budget Watch Collecting/Unknown Swiss Made
"I've checked Google, and can't find any information on my watch--The brand is AcmeTime, marked R-Swiss-R at the bottom...."
The bad news is there were thousands of these brands with almost no information available. The way the Swiss watch industry worked was that there were a very few companies that made most of their own parts--Most bought either complete movements or Ébauches ("movement kits") from one of a few movement houses (now mostly owned by the Swatch group), and frequently bought cases from someone, and dials from someone, and... Sometimes these would be assembled by the brand, other times they were assembled by someone else.
This isn't unique to the Swiss--American watch companies worked in a similar way. When you bought an early Elgin or Waltham pocketwatch, you usually bought a movement with dial and hands, and had it cased by your local jeweler in a case of your choice, sold by an unrelated company. The difference here is that your watch would be known as an Elgin, rather than by the name of the casemaker or whoever assembled it.
The good news is that you can usually identify the movement used in these "generic Swiss" watches, and that will give at least a few clues as to quality, market and era. Most of these will have a movement number--Usually under the balance wheel, sometimes on a bridge and occasionally on the dial side of the main plate. Roland Ranfft has a great Movement Database with a search feature and great illustrations--Type whatever you think the number is, and see if it matches the picture.
Incidentally, the R-Swiss-R is a clue that the watch dial is before 1968, and likely sometime in the 1950's or older. The R stands for Radium, used to make the hands glow in early watches. In many ways it was superior to modern glow, as it would glow for years without exposure to light. Unfortunately it is also slightly dangerous. Radium was replaced by Tritium, a weaker and much, much safer radioactive compound, and later by Luminova and Lumabright, phosphor-based chemicals that will glow for many hours after brief exposure to light. Some replica watches will have Tritium markings, even though they use non-Tritium lume.