Paper towels last a long time at my house (a couple of years, at least, per roll) because I use these 99.9% of the time:
Those are well used, fraying towels cut down to approximately washcloth size. The edges won't fray because I do the cutting and hemming on a serger. The advantage to this size is that dish rags, washcloths, and my cleaning cloths fit this handy cleaning tool...
...purchased at a thrift store. No disposable Swiffer cloth has never crossed my threshold. If you noticed all the dangling thread chains, well spotted. The last two steps in cleaning cloth creation are dabbing on Fray Chek to lock the threads, and after that's dry, cutting the threads off.
Some of the cloths are much smaller—as small as 3x5 inches—because I had to work around holes or tears. These mini rags are also handy; one resides with my spinning wheel.
I see a number of other knitting bloggers post about knitting swiffer cloths, but I bet if they had a serger they'd be using it this way, too! Here are more swiffer options that Google revealed.
My cleaning cloths collection does include several old knitted dishcloths which do fit my swiffer and do a great job.
Cheerios for now!