I can describe the sound of minute repeaters probably more thoroughly as I describe the tasting notes in wine. Hence why I could be a watch sommelier, but I haven't passed the basic certification for a wine sommelier by the Court of Master Sommeliers. But main things to look out for is tone, volume, and speed. Within tone, you're listening for tuning, melody, and thunking. Volume is how clear the sound is both close to the ear and at a 1 meter distance. Some watches are rather loud close to the ear but unusually quiet a meter away, ideally you want one that's loud. One other thing about volume is how loud is the chime and how loud is the mechanism. The mechanism produces a whirring background noise, which is undesirable. This is due to the fly governor spinning inside the watch (IWCs have quite noisy fly governors). So you generally want to measure the total volume of the piece then minus the "noise" to get the "net volume." Finally speed. The 12:59 sequence should be done in 17-19 seconds. Ideally around 18 seconds. Pauses between the hour strikes and quarter hour strikes should be noticeable but not too long. Now, let's say there are only hours and minutes, say 12:14, thus no quarters. Most watches would take an extra long pause between the two. The pause shouldn't be so long that you think the sequence is over and you thought it was 12:00. So all of these considerations are a part of speed.
There are other issues with minute repeaters as well. For instance servicing them. Some brands, once you service them, they sound completely different. Sometimes better, sometimes worse. Patek Philippe and Vacheron Constantin actually record the original sound when the device left the factory and after servicing the watch, they try to make it sound somewhat close to that original sound. So this is something to consider.