First problem to be considered np complete?
You can find the original paper of Cook online: The complexity of theorem-proving procedures. You can also find Levin's paper in Russian: Universal Sequential Search Problems. A translation can be found in the appendix to a historical survey by Trakhtenbrot: A Survey of Russian Approaches to Perebor (Brute-Force Search) Algorithms. You can even find Karp's Reducibility Among Combinatorial Problems.

Cook showed that the set of DNF tautologies (i.e., the complement of SAT) is NP-complete in his sense (oracle reducibility). Karp mentioned that SAT is actually NP-complete with respect to many-one reductions. Levin's paper mentions six different problems, but has no proofs (as was customary).