Hellobee Boards

I love PBK too, but if you're looking for super soft, I would get cotton jersey sheets!

http://www.bedbathandbeyond.com/store/product/pure-beech-reg-jersey-knit-sheet-set/1309773?Keyword=twin+jersey+sheets

They're not fun kids sheets, but I ordered these for our new bed and have loved them! They're really soft but really affordable. http://www.amazon.com/gp/product/B00AMNAMVC?psc=1&redirect=true&ref_=oh_aui_detailpage_o02_s00

Have you tried homegoods or TJMaxx?

@mediagirl: I got a set of the "t shirt sheets" (cotton jersey) from Target for our king bed. They were meant to be temporary but OMG they are our favorites! They are so so so soft and I think for a king it was like $30-40 so a twin would prob be super cheap! I loved them so much I found the Burts Bees version for my sons crib.
ETA: these are also amazing but I do sometimes get hot in them so maybe they're better for cold weather. But they are what a lot of high-end spas use on their massage tables and I was always like "these are amazing" they almost feel like a super super fine velvet. so finally one day after my massage I searched for the tag and found they are called "Comphy" and confirmed other spas I went to use them. So I found these on Amazon and they aren't the Comphy brand (they are $$$$) but the same feel! I'm also obsessed with them, it feels soooo soft and luxurious.
http://www.amazon.com/gp/aw/d/B00C3MUK4O/ref=mp_s_a_1_1?qid=1439554133&sr=8-1&pi=AC_SX200_QL40&keywords=comphy+sheets&dpPl=1&dpID=31ve%2BFs2i7L&ref=plSrch

Stick with Target, but not the kids' section. Cotton jersey is the way to go. There are usually some nice solid ones in the main linens section.