Which sodium citrate is used in silver nanoparticles production? In my studies, I have a group project to realise: to make some $\ce{Ag}$ nanoparticles using Turkevich method (boiling $\ce{AgNO3}$ with sodium citrate in water). In most of articles authors write about using sodium citrate solution, but when I searched for this compound on Sigma-Aldrich, they offer me a wide range of compounds named "sodium citrate". Mono-, di-, tri- sodium citrate.

Searching for a more specific description, I found this article:

http://www.sciencedirect.com/science/article/pii/S1878535214003645

Here they wrote citrate's formula. It is tri-sodium citrate. But Sigma-Aldrich offers it in hydrated versions. Which version should I use? Is hydration even relevant when I'm going to boil it in water?
You can use hydrated tri-sodium citrate, it's readily soluble in water. As for its chemical reactivity, it's identical to tri-sodium citrate.
You should take into consideration the increase in the molecular weight in the hydrated form due to the presence of water molecules.