the deeper the better. depends what you are using it for. if it is to keep weeds down as a mulch 2 - 4". If its just as a surface dressing to make it look nice about an 1".
welcome to GoY too.

The texture also matters, Iris. The coarser the bark, the deeper it needs to be to give good coverage.

Mine is the Dark type and the larger peices 4-5" deep along some borders that contain shrubs and on a path of the larger Golden type also 4-5" deep . After about 3 years I needed to top them up. I do rake it back to put granular feed around my plants in the spring and then rake it back again. The rest of the season I liquid feed. The path I just rake over in the spring or as needed. I found the Golden type became the same colour as the Dark type after quite a short time!

cheers