The closest I can find to your needs and one that would allow you to start your set without regard to coins being either PCGS or NGC is the NGC Registry "19th Century Series Type Set, Non-Proofs Only - No Gold". It does not include 1900 as part of the 19th Century. But it does not require proof coins or gold coins to complete the set.
Another interesting type set is the 7070 No Gold set. It's the equivalent of the Dansco 7070 album. It's a nice fun set to play with.
Whatever you decide, I hope that you have fun with it. I don't do the Registry Set thing to be competitive, it's just a nice way to track what I'm collecting and give me easily documented targets.