I agree that you have drawn the drawers too tight in their openings. I’d do the following:
- reduce the height of the entire drawer box so that it has at least 1/8"-1/4" clearance at the top. Tighter really isn’t necessary, increases the risk that if the step sags it will bind, and increases your need for precision without really providing a useful increase in drawer capacity.
- as @DaveR suggested, add some sort of low-friction material to the bottom edges of the sides.
- reduce the width of the box to leave maybe 1/8" clearance side to side. Again, closer has a high risk of binding especially if everything isn’t perfectly straight (and stays that way with use). If you want, you could also apply a low-friction material on the sides.
- raise the bottom of the drawer up perhaps 1/4" from the bottom edge of the sides so that the entire surface doesn’t bear on the board below, just the edges of the sides. Move the bottom edge of the back up similarly and adjust the height of the front. This will greatly reduce the drag when you slide the drawers in and out.
- raise the bottom edge of the outer drawer front by about 1/16" so that it doesn’t drag on the board below. You can leave the top edge flush with the step above.
- depending on whether anything will be adjacent to this (e.g. a wall) you might want to reduce the width of the outer front a bit so that it doesn’t rub against the wall.
I notice the unit is 12 7/16" wide. Is there a reason to choose that particular width? Not saying it is wrong, just wondering if it is necessary.
I would probably do various joints differently (again as @DaveR suggested), but as you are a newcomer to woodworking I’d rather you get the pleasure of making something and learn about more advanced techniques as and when you have time.
Edit: a further thought - how will people grasp the drawers to pull them out? You may need to add some sort of finger grooves or pulls.