Basic Overview
I've learned from the Phantom Menace that Jedi garb can be quite varied in color, material and style. For now I am going to focus on the style worn by Master Jedi Qui-Gon Jinn and his padawan Obi-Wan Kenobi. From what I have learned so far, the Jedi outfits seem to consist of 6 basic parts. The inner tunic (layer 1), the tunic (layer 2), the tabard or vest (layer 3), the pants, the obi or sash, and the outer robe or cloak. Other misc. items include the belt with pouches and various equipment (which I will post in the replica section as items are completed), boots and of course a lightsaber (see lightsaber section).
Fabric Recommendations
Qui-Gon's Tunic, Inner Tunic, Tabard and Obi/Sash appears to have been made out of Raw Silk also called Silk Noil. Leiasky pointed out that Obiwan's Tunic, Inner Tunic, Stole/Tabard, Obi/Sash looks as though it was made from wool gauze although a medium weight, ivory Linen (lightweight for the inner tunic) would make a good subtitute.
Both Qui-Gon's and Obi-wan's pants appear to have been made using a medium to heavy weight Habotai or Silk Broadcloth (at least 16mm).
The Cloaks were made of Wool.
Since Linen and Silk and Wool are not within everyone's budget, consider using a medium weight cotton or natural unbleached muslin. Try to avoid synthetic fabrics. They are much hotter and do not allow much air to circulate. With three layers and a Cloak using natural fibers will make a huge difference in how comfortable you are.
Tip from Anna - : Where you have suggested linen, calico makes a very cheap alternative (costs less than UKP1.50 a metre over here), just wash it before cutting out the pattern, as it shrinks the first time it's washed.