There is so much variation in snowpack and melt from season to season and place to place. Most years the hiking in the Purcells and Rockies is good by mid-June but you will be crossing some snow patches at higher elevations and you likely know this can be hazardous in some sections of trails. It has been so long since I hiked in the coast ranges that I can't give any honest input there about snowpack.
This season we already have a meter of snow at 7000 feet elevation and above but have little or no snow at 6000 feet or below in the southern Rockies and Purcells. The forecast is for cooler and wetter weather in the early winter than usual meaning a bigger snowpack.
Something to factor in is the absence of National Park fees in 2017 likely meaning higher usage than usual and fuller campgrounds than usual. This would not affect the coast as the parks there are Provincial. It might be wise to start in the Rockies since you would be there before school holidays and might beat some of the crowds.
Enjoy!