If I were starting out, like you are, I would get a No. 5 Jack Plane as you and others have suggested, and I would get a second iron. On that second iron I would grind it in such a way that the middle inch is flat (the way it came) but the outer edges have a pretty significant radius, back a full 1/16th-inch at least. This allows squaring a narrow edge essentially flat, but with the radiused edges you can take a deep cut like a traditional jack plane to flatten and thickness quickly. The other iron I would reserve for smoothing so just break the corners, ever so slightly, so it doesn't leave tracks. This will work as a smoother, and can work on a shooting board as well.

There are other planes that can do these jobs better than this, and you will soon grow tired of adjusting the frog and chipbreaker for this or that and swapping the irons, but this will get you started.

After that, invest in some sharpening equipment, (more important than the specific plane you wind up with, IMO) and a good straightedge. You can make a longer straightedge, squares, and various other tools you will need, but this will get you started.

DC