That's not a bad method.
I generally put it on paper towels, and put a meatloaf pan full of water on
it. I leave it over night.
Or I stick it in a coffee filter, like you'd be making yogurt cheese, put
another filter on top, stick something heavy on top like a jar of pickles.
The coffee filter sits on top of a bowl or jar very well.
As for lint on the dish towels? Wash 'em, then use them.
I also freeze tofu first, then press it. Freezing gives it a firmer
texture, and after freezing and pressing it, it's a good, almost crumbly
texture.
This is called "salt and weighing" when you do it to cucumbers. The salt
brings the liquid out of the cucumbers, pressing it squeezes it the rest of
it out.
Hope this helps,
Christine