I alternate layers of newspaper and white copy paper (or colored copy paper, whatever ...), then usually finish with a detail layer of paper mache clay, if I want a smoothish finish (like pumpkins), or crumpled newspaper if I want a more wrinkled look (like gargoyle wings).
I find copy paper actually stronger than the newspaper, but I like the size of the pages I can get with newspaper ... so mixing them works for me. (I don't tear my stuff into strips -- I paste 1/4 pages of newspaper with whole sheets of copy paper and then tear them (or not) into the shape needed after it's pasted. Wet paper is easier to tear.)
The paste I use is ~ 3/4 methyl cellulose, and when I brush it on the paper, it 'softens' it ... so I can get newspaper to drape like paper towels if that's what I need. I'm with Spooky and do my papier mache in the basement with fans and dehumidifiers and pieces normally dry overnight, or within 24 hours.
You can see more info plus get my recipes in the skeleton and skulls tutorial I posted:
(scroll down to post #7, "skull tape copying part 2")
If you're looking for a faster drying method using paper towels, Jonni Goode at Ultimate Paper Mache has a plaster + glue recipe that she uses in her masks.
Jonni also has been known to put her paper mache in the oven in order to speed dry it. (Obviously it shouldn't have any plastic in it or anything like that -- and it should be <=200 degrees.)