This doesn't answer your question, but before sending off my first puzzle to an actual publication, I would seek feedback from people on this list or other resources. You'll get much more rapid feedback (days instead of months) and you'll improve/learn a lot faster that way.
In general, most outlets give responses in 1-5 months nowadays, and time to publication can be 3-10 months I'd guess. NYT and LAT are the slowest in my experience.
The list on cruciverb.com is pretty out of date. The actual list of publications open to the general public I think is:
NYT
WSJ
Atlantic
Universal
LA Times
Newsday
Fireball
Crosswords Club
Spyscape