The first newsletter I sponsored was The Slice, for just $10. That got me 8 mailing list signups.
So next I tried Indie Letters, for $50. That got me one product signup and another 8 mailing list signups.
While that was a good educational experience I'm done with newsletter sponsorship. Content marketing and participating in online discussions proved a far more effective marketing channel for me.
Other than the costs, sponsoring a newsletter is abour a half hour work. Additionally, unfortunately it seems to be industry standard that newsletters won't send you an invoice.