The Home Depot stores I've been in have sold three kinds of hardwood - poplar, maple, and red oak. Closer pictures would be needed to tell for sure but I don't think that door looks like any of those woods. Of the choices, for a clear finished oak or maple would be the better choice. For paint, maple or poplar.
Making a full size door is fairly advanced woodworking and a successful project would necessitate a complete shop including tools like a jointer, planer, tablesaw, router and router table, blades and bits, plenty of clamps, sanders, and a large flat table to glue up the door.
In terms of actually making the door, most interior doors are 1 3/8" thick which means you'd start with 6/4 stock (1 1/2 thick) and mill it down to the final dimensions for the stiles and rails. A profile milled into the stiles and rails. I can't tell from the picture how the slats fit into stiles but mortises (or something) would have to be cut for those as well. Then everything is glued up, sanded, stained, and finished.
Thanks, going back on what you said about tools needed and how everything is joined, I'm looking to make something as similar as I can. Currently I have only a 2 1/4 router and table, circular saw and a sander....nothing crazy. My current door is 1 3/4 thick so 1 1/2 might not be so off. This for my apartment so it doesn't have to be best, just better. I would buy a door but my current doors are not normal dimensions and paying for custom doors is out of the question.
Any kind of jointery requires flat, square stock and while "a little bit" here and here might not seem like it matters, when you put the pieces together they won't quite line up. That becomes very frustrating very quickly and for some things you can be a little less precise than others. Let's say you're making a coffee table, if the top is a little longer or one edge isn't quite parallel to the other, most people aren't going to notice. For something like a door that fits into a frame, those errors will become quite apparent. The same is true of cabinetry. Building one kitchen cabinet isn't that difficult, the real challenge is building 20 with identical dimensions.
For a 1 3/4" door, you'd start with 8/4 stock which you aren't going to find at Home Depot in the sizes you need. Better lumberyards will have lumber that thick and some will even dimension stock, for a fee. You could use a mortise/tenon to join the rails and stiles instead of using an expensive ($150) router bit set to cut the cope/stick joint. That would give you a plainer door, often called a "Shaker" style.
You can even dress up the edges using some kind of profile bit (round over, ogee, etc.) but you won't be able to get into the corners fully. So it looks like that's what you did (vs. a true cope/stick joint), although you can dress it up little by hand using a chisel and sandpaper.
You could do something like this by eliminating the panels and increasing the number of stiles:
If you want to go the "Shaker" route, you have some other options for jointery. You could use biscuits or something like Festool's Domino system. You can probably find a decent used biscuit jointer on Craigslist or eBay. Festool tools tend to have a really high resale value, so you could by a Domino, use it once and sell it for 80% what you paid for it. If you were doing to paint the door, pocket screws might even work. You'd have to fill the pockets and while they do sell plugs those would be very noticeable on the surface of a door if you used a stained finish.