It is my understanding that most Newspaper ink is now Vegetabe Based, as opposed to Chemical Based. I believe that most Magazine ink is still Chemical, so I would stay away from that.
I never liked Peat Pots for starting seeds. When I did use them, I tore them apart before planting and threw them away. They never went in the ground, but that is my preference.
Now I use empty cardboard egg cartons to get the seed started, then I transplant them into 4" plastic pots until the plants and conditions are ready. 4" pots or bigger give the roots plenty of room to grow and not stunted for the few weeks they are in there. The more root system you have, the healthier and bigger the plant is.
You can get root bound in a smaller peat pot. One year I just punched 1" holes in a bag of Potting soil and started my seeds.