Best time to layer is when you have a suitable tree, some time and all the things required.
Second best time is spring when you have a full growing season ahead to get roots.
There's no rhyme or reason to how long it takes a layer to root. So many factors affect it - species, timing, technique, health and vigour of the tree, location, etc. Just check every month or so to see if you can see roots growing. Clear cover on the layers makes that easier but you can also gently open up and check without damaging the process. Alternatively, where checking is not easy, leave it until mid to late summer before making the first check.
3" branch is likely to take longer than smaller wood. It may even take a year or more.
Remember that junipers don't always bud on bare wood so I hope the chosen branches have some green nearby to chop back to. Thicker is not always better for bonsai.
My experience has been that branches in a tree look really great. Up closer while you are layering the potential appears less. After it has been cut off and potted you'll wonder why you even bothered. The vast majority of layers I've seen actually have poor bonsai potential so be very choosy when selecting layers.