So I was thinking, instead of purchasing a dedicated (and expensive) whetstone with limited coarse(ness?) range, why not use patches of sandpaper in increasing grit numbers (getting finer), stretched on some small flat surface? This way I can have as many grit steps as required, to the fineness level required, for relatively cheap and disposable?
Yes, I've heard this suggested, using wet/dry sandpaper and a mousepad. It is a very inexpensive way to match a whetstone, and you can use sandpaper with the same grit to produce an excellent edge.
You duct-tape the sand-paper together so it wraps around the mouse pad, and then pull the knife along the sandpaper with the edge trailing. This is to say, you use sandpaper in the opposite direction as a whetstone. Once you work up to the finest-grit papers, you can use jeweler's polish and a leather strop for a truly razor-sharp edge.
Because the mouse pad's rubber/foam has some give, this method produces a convex edge which remains sharp for longer that an V-cut, because it has more metal behind the edge. It also still presents a very sharp point for cutting, moreso than an equivalent V-cut front bevel.
Using sandpaper will also cost a small fraction of what you spend on a good sharpening stone, which will run you $50 or more PER STONE.
Name / US Grit Rating / Use
Source: Sandpaper-mousepad sharpening
Edit: Another way to use sandpaper in sharpening -- expanding the grit range for a Spyderco Sharpmaker
I'm currently using sandpaper to make a very coarse stone for sharpening extremely dull edges on my Spyderco Sharpmaker. I wrap both of the normal triangular stones with a strip of emery cloth or 220-grit wet/dry sandpaper, and then hold it in place with medium binder clips. Since the lowest stone the Sharpmaker comes with is 800-grit ceramic, this saves HOURS versus using the normal stones. It is also considerably cheaper than the diamond stones they sell; for a big tub of clips and a package of sandpaper, I paid $7, versus about $37 for the diamond rods.
I bought my (Chinese) whetstone for 7,5€ and I've used it for the last 20 years.
You could spend some money on a honing steel, but even these are not really expensive. I got mine for free at a fair, and it receives regular action.
Make sure you buy cheap vanadium steel knifes for your kitchen (shameless self-promotion).
If you're looking around your house for stuff you already own to sharpen your knife on, the story goes that the underside of a dinner plate is the way to go. I've never done it - I bought stones from Lee Valley many years ago and I have a steel, and between them I'm taken care of.