Some manufacturers offer packaged "wood finishing cloths". I've always used old towels, old shirts, or paper towels both for applying certain finishes as well as when wiping off excess. Do "wood finishing cloths" offer much advantage over using whatever is relatively clean and laying around for either of these applications?
I've used both and haven't seen any real advantage to the manufactured ones. In fact, I seem to get better mileage out of my polyurethane by using a bit of old sweatpants material cut and sewn into a tube. It fits my fingers well, holds more finish before having to re-apply to the rag, and the outside doesn't deposit lint; it's convenient, and seems to use less finish than the manufactured fabrics since you're not soaking the whole rag, just the surface area you're using to wipe with.
Main advantages of the manufactured ones is that you know they're low-lint, you don't have to worry about color bleeding out, and if you're doing a lot of woodworking you might run out of houehold rags.
On a slightly related note: microfiber cloth seems to be as good as a "tack cloth" for removing dust before finishing, and can be washed and reused many times.
I once found a roll of cheesecloth in the dumpster at work and took it home for finishing projects. I liked it because it was rolled up like paper towels and the individual pieces were separated (about the size of a roll of paper towels). I could just grab one when I wanted it.
They worked well but no better than the cut-up T-shirts or old cotton socks that I usually use. By the time I retire a pair of socks, there's little fuzz left to become lint. If there is any lint from a T-shirt, it seems to come from the cut edges which I manage to mitigate by folding the cut edges under when I roll up a piece.
I would say there are 3 considerations
Lint: The smallest amount of lint will make a finish bumpy. Provided you know which types of cloth will or won't leave lint, I see no benefit in the manufactured ones.
Absorption: Some fabrics have too much of a synthetic fiber content and won't hold enough of the finish to be useful. They can have a 'smearing' effect. You'll know as soon as you try something like a sock with poly blend.
Supply: I have no lack of household cloths. My favourites are dish cloths and dish towels. If you have a supply problem, then you can either buy manufactured ones, or spend $2.00 on some flea market t-shirts.
So the first two considerations are a matter of experience.
The third is the only reason I would suggest buying manufactured cloths.