So, is there a recommended program/method for ripping ISOs of CD and DVD-based games, in order to get a 1:1 copy?
AFAIK, there are a bunch of methods, but they're all basically the same.
CUE/BIN was an old standard that created a large "binary" file, and a tiny "cue sheet" which was basically instructions on what to do with the binary. (IIRC, using this standard to create a 1:1 copy was what defeated early CD copy-protection, which was achieved by varying the amount of empty space between the tracks. If you simply copied the data tracks off the disk and burned those individual tracks to a CD, the CD would fail because the empty space was wrong. You needed a perfect 1:1 copy to get around that clever protection.)
Then a software program called "CloneCD" came up with their own format called CCD/IMG which created a large "image" file, along with a tiny CloneCD-branded file which contained instructions on what to do with the image. It was basically the same thing as CUE/BIN, but self-branded by a popular new program, so people made simple programs that could convert one format to the other (because they're basically the same thing, and you could convert from one to the other while still having a 1:1 copy of your original game).
Then Alcohol 120% (a "virtual drive" program you could install on your PC so that ISOs loaded into the program looked and behaved more like physical disks inserted into a physical drive on your PC) invented another new standard called MDS/MDF. It does... you guessed it, the exact same thing as CUE/BIN and CCD/IMG.
Whatever program you use to create an ISO, it should be able to make a perfect 1:1 copy, with an insignificant detail in what format your program decides to use for the ISO. Emulators like ePSXe hardly bat an eye at the various different formats, because they're all basically the same, so they're all supported in the emulator.
I don't know which ISO ripping programs are currently popular, as the last time I ripped an ISO was back when I was using Windows XP.