Walls – What options are available for insulating interior walls theself with minimal damage to the 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.

I think based on the comments I better understand your scenario now.

Building Science has a lot of great information on basement insulation and the suggested method is to use XPS foam against the walls, optionally bats between the studs and no vapor barrier (since the XPS foam is the vapor barrier).

I would suggest that you use 1 1/2 - 2" XPS foam against the walls, and then space your studs another inch or so away from the wall (to allow your water to drain). If you need higher R values then the XPS provides you can use bats between the studs and I would suggest something like Roxul insulation which is stone wool instead of fiberglass since it is not affected by moisture like fiberglass is.

It would also be advisable to use steel studs so that they don't rot should they come in contact with moisture. You might also opt to put the bottom plate on top of a piece of XPS foam so that there is a less likelihood of the metal studs rusting.