I've done the TMB and if you're planning to hike the route anticlockwise (which I think is the best way to do it) I would suggest that you start at Les Houche. If you decide to start at Chamonix you will either have to walk UP to the walk, (a zig zag slog) or catch a cable car and then going the anticlockwise way around you will then have to walk DOWN to Les Houche. Personally I'm glad I did this down route to Leas Houche on my last day because it finishes at the train station. Then, to get back to Chamonix you can walk (very easy) or go by train, equally very easy.
I've walked the TMB both ways round, preferred the anticlockwise. Luckily I had really good weather both times.
You will have to make one important decision on your way around, but not until you get to Champex. Do you hike over the Fenetre d'Arpette varient route, or take the more northerly official route? Both to me are equaly good but they are different as well. The varient is over a mountain, the northly route is more footpath and green, with a Refuge en route just in case you need a beer by then! If it was me and doing it for the first time I'd hike the official route.
En route I found that I could often, when high up, could drink the water straight out of the streams or out of pipes, some are marked as OK. Although I carried about 2.5L each day I was never worried about finding water. I would also suggest that you do stay one night in a Refuge, I think they are great fun! Everyone starts the meal at the same time, turned into a great boozy and entertaining evening. I think its the most international of routes, I met people from 'everywhere!' I stayed once in the Rifugio Bonatti, a really great setting. Mont Blanc is at this point 'in your face' the bulk of it in front of you is stunning! If you want to wild camp as I did the second time, but just have the meal, there is plenty of flat grass areas about 200 - 500yds before you get to the Refuge.