Starting Point is usually Sarchu (when coming from Manali) or Brandy Nalla (coming from Leh). This river trip lasts for 3-4 days and will lead you directly into the Zanskar, so a joint trip is great and u can easily restore your supplies in Padum.
The Tsarap needs to be fully self supported and should not be underestimated. The starting Point is in 4300m and you should be properly acclimatized before starting.
So better stay 2 days in Sarchu (pretty boring tented camp) before you put on. All gear and food (noodles and vegetable can be bought in Sarchu to inflated prices) has to be brought from either Leh or Manali, so make sure you didn't forget anything, as up there nothing is available.
Once on, you will only see some small farming huts and the first real 'village' is the monastery at Phuktal. After that there are some settlements, but it is hard to get food or supplies there.
Padum is the first reliable place where u can get food and the bits and pieces to re supply for your journey down the Zanskar which the Tsarap joins just after Padum.