I've done the Wonderland Trail-- it's amazing!
The right time of year is all about snow depths, but generally speaking, August is the best. The reservation system is important, so you need to get on your game in February and be ready to submit for the lottery (I think) in early March. Walk-up permits are also doable if you have a small party and flexibility with your dates.
There's no "best route" because it's a loop around Ranier, but there are quite a few trail reports out there that suggest certain campsites in a certain order. Longmire is the most popular starting point, going counter-clockwise. The permits are based on campsite availability, and you have to use established, numbered sites. We talked it over with a park ranger who gave us recommendations on sites and lengths between them based on our ability level (mileage/day).
Here are some resources we found especially helpful:
It's such a great hike-- it's very safe feeling, yet also very wild and challenging. You can store food caches by mailing boxes to the NPS so you only carry 3 days of food at a time <-- amazing! We did it in 9 nights / 10 days, but we also pride ourselves on complicated meals and luxury items 🙂
Have a great hike and let me know if you need any help planning!
I have been thinking about hiking the Wonderland Trail as well. I purchased a book off of Amazon called Hiking the Wonderland Trail: The Complete Guide to Mt Rainier's Premier Trail by Tami Asars.
It has a lot of great information and is a great read. It covers the permit system, recommended gear, food caching, great trail and campground details, maps and some gorgeous full color photography. I've read the book multiple times - it's that good!