What processors are available?

Yeah; the instructable specifically mentions what I call "The $100 paradox." You can build your own computer from scratch; make (or have made) a PCB, buy individual chips, etc. It'll probably end up costing you about $100 for the pieces and equipment and stuff.
Or you can get some commercial stuff that is re-purposeable into a general purpose computer. It'll probably cost about $100. (Chumby, for example.)
Or you can buy one of the more extensive existing development boards (hawkboard, beagleboard, etc.) They're about $100.
Or you get get a low-end palmtop, or a used last-generation desktop. They'll probably run about $100.

Which of those is your best option depends on exactly what you want to do. It's VERY difficult to beat the "value" of a used desktop computer (frequently available for FREE.) But they won't fit in your autonomous air vehicle...

One reason that Arduino is so popular is that it's only about $30. (Though if you add a motor driver and and xxx shield and some other stuff to bring it up closer to the more complex development boards, it'll likely cost ... about $100.)