Reddit mentions of AMC Map: Presidential Range: White Mountains Trail Map (Adventure Series)

This is the White Mountain map I use, along with the AMC White Mountain Guide.
There is also this map of just the Presidential Range.
I don't think any "serious" maps will have interesting information besides trail names and distances. If you want to read thorough descriptions of the trails they I seriously recommend the AMC White Mountain Guide.

For maps, Caltopo is pretty thorough in that area, although it's kinda hard to read. If you want a physical map, this one is only $9 on amazon.

They provide mattresses and blankets there, but they ask that you bring sheets or a sleeping bag and probably pillow cases. You could just pick up a really cheap set of sheets at walmart or something once you're in New England. Other than that you'll just need clothes, rain coat, head lamp, first aid (stuff that's east to fly with) and lunches/snacks. For the clothes, even though it's a fully enclosed building you'll still want layers in the white mountains (fleece, long underwear or long pants and a light hat is what I'd recommend).