Floor standing U wood frame built at home - what to use for a 90 degree joint?
As described, there will be huge issues with racking - the tendency for this to want to collapse onto one leg or the other, no matter what fasteners are used.
If you'll take a look at any flat pack furniture, you'll see that they come with a back, often nothing more than cardboard. One might think that the back is provided to keep things from being pushed off the back of the shelves and falling behind the cabinet, but the back is really to prevent the whole thing from collapsing sideways. The fact that it keeps you from pushing your shirts behind the wardrobe is just a bonus.
If you were able to find flat angle brackets:
Image courtesy of walmart.com. First somewhat small image I found for what I was after.
that were long (I'd suggest 12&quot; legs or more), with legs that were only 3/4&quot; wide so that they would hide against the edge of the particle board, then attach them with screws designed for particle board, you might have enough rack resistance to get this to stay upright for a while, but it will still want to sag and warp eventually.
You're going to need serious corner bracing (straight pieces or triangles that connect the top to the legs at about 1/3 the length of the top - roughly 20&quot; across and 20&quot; down) or something like a shelf support bracket or a full on back in order to keep this from collapsing.