Why would you use paper towels? Either use a cloth tea towel or let them air dry in a dish rack.
For dish towels to become more absorbent they need to be washed first, without softener in either the washer or the dryer (sheets). When first purchased, they have starches and finishes on them from the manufacturer and these prevent them from soaking in the water. The more they are washed, the better they work. All cotton work the best. I buy the white bar towels at our dollar store and they work very well and are both more economical and more environmentally friendly than paper towels.
If you do decide to go with paper towels, at least re-purpose them after using them to dry clean dishes: drain bacon/sausage, wipe up spills, clean counters, pad dishes, dry them out and use them again.
I buy Scott towels at Family Dollar. You get 10 rolls for $10, which lasts our family ( of 4) about a month. Keep your eye on thier sales, from time to time they have them for $9, plus if you can find a coupon you can save even more. Possibly getting them as cheap as seventy cents a roll. If you save box tops for your school, one can be found on the package.