What glass for an interior, mainly glass, wall?
If it is in a frame 1/4" glass will be sufficient.  Your options for glass will be tempered glass or laminated glass because of it's proximity to the ground.

Tempered glass will break into very small pieces like a car window for a door.  Tempered glass is stronger than normal glass.

Laminated glass will break like a car windshield.  It breaks normally but it is two pieces bonded together with a plastic.  The plastic prevents most injuries as well as the mess from breaking.  Laminated glass is more often used for safety/security applications.

Although 1/4" is suitable for the application, I myself am always weary installing it as an interior partition.  My family business has built all glass offices in buildings and we use 3/8" tempered glass.  3/8" Tempered is extremely difficult to break.  When you get up to thicknesses that large as far as cost goes the difference between 3/8" and 1/2" thick glass isn't very significant.

If you go with a thicker size be sure that your trim is strong enough to withstand an impact of the weight of the glass, the weight of a person, and the velocity they are traveling.  This is due to the fact that it is more likely to break from breaking out of its frame and falling down, especially in wood.

If the beams are not structural I would recommend you use a router to create a slot in each beam deep enough to slide the glass in far enough to place it where it needs to go and then slide it back towards the other beam into the slot you created there.  This is commonly done with metal storefronts and is called a flush glaze.