[dustmaster]

Ah... the innocence of the question, "I just want to do one small thing.."
Before staining I would suggest using a wood conditioner, especially on pine. You can get it at home depot and it helps the stain be absorbed more evenly.
Perhaps you should us a vacuum on the wood to help get rid of the dust.
One big question I have is: Is this a single piece of 1X12 and 1X10? You will need to rip and laminate wood this wide or it will warp. You can buy pine shelving from HD that has already had this done as well.
OK, so now you are ready for the pretty routered edge... I suspect the 1X3 poplar that was mentioned is to tape to the one side of the router so it isn't too tippy while you are routering the sides of your shelf.

Try everything on a test piece first!

 

[dustmaster]

I believe all wood this wide and thin will warp. It basically will over time want to be as round as the tree it came from. You will need to rip the wood into 3 inch pieces, joint the edges then flip every second piece so the grain runs opposite to the piece beside it, then glue and clamp, then sand, and sand and sand...
Or just buy the pre-glued pieces until you get all the wood working equipment to do it yourself.