For your window boxes: Drive to Home Depot. Go over to the drywall section. See if they have a mud trough that's about the size you want to make your planters. Buy one to use as your tester. Make the box just big enough to drop the mud trough in there.
If'n you don't like that idea, or they're too expensive for you to drop in a flower box, head over to the heating/ventilation aisle and pick up some galvanized sheeting (and a pop rivet gun and a tin snips if you don't have one). Make a box out of the galvanized sheeting as large as you need, and throw some caulk over the seams and rivet heads. Then make your window box and drop the metal box in there.
I'd always look for ways to NOT have dirt touching the actual wood. The exception to this would be the oak barrel types of planters, but for window boxes, they'll last FAR longer if you don't have moist dirt pressing against them 24/7 during the growing season. Lasting longer means you don't have "rebuild more flower boxes" added to the honeydo list as quickly in the future.
Also, and it seems like it'll be a waste of money now but will pay off in the long run, build several more window boxes than you need right now. Stick the 3-4 extras up in your shed. Your wife will invariably want more of them after she sees how nice they make the house look, and/or you'll have to replace them.
If you've got lots of plywood left over, use it to make a template for your flower boxes. This will make it quick and easy to make hundreds of duplicates that are exactly identical. After you've got the pieces cut to the correct size, fill the edges with either bondo or drywall compound. Keep filling and sanding until your edges are smooth and void free. I'm telling you to do this simply because it's what you've got on hand, but honestly, the best thing for you to do is pick up a half or quarter sheet of MDF at Home Depot and use THAT for making your template.
As for the joints for that box, it's a nice small project, why not consider trying your hand at a sliding dovetail joint to attach the narrow side pieces to your front/back piece? Also, a rabbet around the lower section with a piece of plywood should work just fine. Just fasten 3 of the sides together, and slide the bottom into the rabbet. Make the rabbets on the two short side pieces a bit deeper so you can slide the bottom into that while attaching the final end piece, then slide it back to catch on both short side pieces and throw a nail in there to keep it in place.
The dado is the better joint to use because of the rabbet (no need to cut one groove deeper than any of the others; I'm just suggesting a dovetail for some practice for you.). Alternatively, you could dovetail one side, and dado the other, but it'll look funky.
I'd also get some very good primer and apply two coats, then top with the color of your choice. Stain will quickly look bad within the first year, even with a spar varnish or other product applied. After one winter, you'll wish you had painted.