Which ArcGIS Online basemap has the best performance in ArcMap?

tl;dr; The performance of all basemaps from arcgis.com inside ArcMap will pretty much be equal.

The basemaps you reference all come from the same cloud infrastructure and show the same thing: static images. (png, jpg, etc).

In short, the only potential performance difference you may encounter is how long it takes to download the cached tiles of one basemap over another. The Light Gray Canvas uses less color and has less features compared to the say the Topo basemap, thus in theory it might be the tiniest bit faster to download because the actual files are smaller. But I'm talking like 1/100th of a second faster.... nothing noticeable.

Note - this answer is specific to ArcMap and consuming basemaps. Newer basemaps are being made as Vector Tile caches which might be a bit 'faster' compared to traditional cached tile basemaps. However, ArcMap doesn't consume (display) Vector Tiles basemaps.

Coming from a remote area with slow and often spotty internet, I have found that it is necessary to set the dataframe coordinate system to WGS 1984 Web Mercator (auxiliary sphere) when using an ArcGIS Online basemap.

Be warned - the basemap loads quickly, but it appears the measure tool does not give accurate measurements when using this coordinate system.

The best resource I've found that can provide an idea of performance and ways to assist is Esri's Technical Guide to Map Service Drawing behaviors of the map service

Basemap layers and map services use a high-performance drawing engine to achieve better performance and drawing quality. This drawing engine provides excellent performance for all supported symbol types.

Because this drawing engine is different from the drawing engine used in ArcMap, you should be aware of some important differences in the appearance of a map drawn in the map service. The Prepare window provides warnings that inform you of many of these differences.