What is considered a standard size map scale?

There is no standard.

However, having said that, if you buy a map book or sheet, there are various scales which are generally used:

1:221,760 (1 inch = 3½ miles)

1:63,360 (1 inch = 1 mile - no longer issued by OS)

1:50,000 (2 cm = 1 km - the OS Landranger series, replacing the 1:63,360 series)

1:25,000 (4 cm = 1 km - the OS Pathfinder series)

The scale chosen depends upon the use.

The smaller the scale (the second number above) the more detail that can be put on the map.

The first example scale above is a map book for driving and generally shows major roads and some minor roads to allow for route planning.

The second/third examples can be used for driving, cycling or walking as they show roads, bridal ways, footpaths

The last example is good for walking as it shows more detail including field boundaries.

Maps with even smaller second numbers are used by specialist surveyors, eg to show property boundaries.

Atlases have a much larger second number.

The larger the second number, the less details that can be put (accurately) on the map.