What size are the standard grids in those roll-up mats people use for D&D 5e and thus what radius / diameter should the base of a miniature be for easy usage?
In the Dungeon Master's Guide, page 250, it states that when playing with a mat the squares or hexes should be 1 inch across and should represent 5 feet. But you can play with the scale of the squares as much as you like.
Miniatures come in varying sizes and they are all described in metric units. For D&D and most other RPGs the most commonly used scale is 25/28mm - this is a scale of 1:64/1:56-58.
Mats are usually drawn with 1" or 25mm grids which are almost the same (1"=25.4mm). For D&D a square represents 5 feet, a scale of 1:60.
These scales are clearly not the same, however, they are close enough. You should have no trouble fitting the base of a 25/28mm mini into a square of this size.