Yes Brian Walks is a very good guide for you. I've also walked the TMB, again starting from Les Houches. Its the best place to begin!
If you are starting from Chamonix, you can catch a bus to Les Houches (not far) or follow a very nice low level footpath from Chamonix which ends at Les Houche train station. That's what I did. I also downloaded the Sity Trail app, the TMB path is shown in great detail (an IGN map) you can also view it on your laptop or PC, its very easy to follow. The reason for starting at Les Houche is that on the LAST DAY its downhill all the way! And before I forget, I suggest that if you do start at Les Houche the best way to hike it is anti-clockwise.
If anyone wants to get back to Chamonix quickly, just catch a bus from Cormayeur through the Mont Blanc tunnel. Drops you smack in the centre of Chamonix.
I camped most days, again very easy, some excellent sites but I also stayed in a couple of Refuges and had a great time! The best one for me was the Refuge Bonatti, the views of Mont Blanc are fantastic. Wished we had meals in the UK like this, everyone around large tables and everyone starting to eat and drink at the same time. The togetherness was brilliant! I was also lucky with the weather, sunny and calm for 12 days. I hope you have the same.
For me the hardest decision was when I arrived at Champex. Should I walk over the col, or take the other and longer route. I took the other route and didn't regret it. I walked over the col the following year when hiking the Haute Route, didn't regret that either!
I found the TMB truly international as well and met loads of people from all over the world. As an alternative if you want to go back to Chamonix again do give the 'Haute Route' from Chamonix to Zermatt a go, a bit harder perhaps and nearly as good.