I can assure you Gmail (and others) will work fine, but it takes some finesse as far as how you're sending those emails.
This
post is basically a starting point but it takes some time to get things configured correctly. In my opinion:
PTR, DMARC, SPF, DKIM are all first-steps in getting email going on a new domain/site.
Just be careful if people try and sign up for mail notifications - lots of bounces will affect your domain reputation. (For those you're not validating, I mean...)