I have said elsewhere that sharpening on sandpaper is the cheapest way to start sharpening, and the most expensive way to continue. That's because you can scrounge up what you need to make a razor-sharp edge on a chisel or plane iron for well under $20. But then the sandpaper wears out pretty quickly, and it retails for around a dollar a sheet. Even if you find it for 50 cents a sheet in bulk, compare that to a $30 water stone that lasts for a couple of decades, and you'll see what I'm saying.
So why bother? Like I said, it's the cheapest way to get going, and you can spend just a little bit to get sharp tools for your first few projects, and then invest in more permanent equipment later on. The cheap honing guide I recommend for beginners will work on water stones or diamond plates as well. And even though I own a set of great water stones, I still use sandpaper when I'm out on an installation and don't want the mess, or the risk of theft or breakage, that go along with using water stones outside my own shop. And wet or dry sandpaper is good for flattening water stones. So when you get additional sharpening gear later on, you don't have to fret about wasting money on sandpaper sharpening.