Mailgun is super cheap and even free if you send fewer than 1,000 emails in a month.
I’ve used Mailjet for my personal Discourse because it’s free up to 6.000 emails a month. That’s far more than I need, but I wouldn’t mind paying if I breached that limit because it would mean I’d built up a goodsized community. 
That said, I don’t see any reason not to try using your HostGator SMTP credentials when you configure Discourse and see what happens.