Have a plan before you start cutting, this will save you from multiple trips to get more wood.
How do you plan to finish it? I would suggest some 80grit and 200grit sand paper and then decide if you want to paint or stain. If you stain its worth using a pre-stain conditioner. If you plan to paint use a primer.
I also find that the quality of wood at Lowe's is generally better for something furniture or finish quality vs Home Depot which only seems to have low quality framing and construction wood. You can get different types of plywood with pre-sanded (you will still need to do some sanding) finishes like Poplar, maple, and oak. It will cost more but if you want this project to last it can be worth the extra, plus it just feels better working with more premium woods, they cut cleaner, sand better, take stain and pain better.
Good luck ~dad