Should you send your newsletter from your own domain?
Yes, if you are serious about it: a sender address on your own domain (newsletter@yourbrand.com) looks professional and has become practically necessary for good delivery since Gmail and Yahoo tightened their rules. Your tool helps with the DNS setup.
Sending from a free address (yourname@gmail.com) is a bad idea for a newsletter: the strict DMARC policies of the big providers mean such mail sent through a newsletter tool delivers poorly or not at all, and it looks amateurish besides. Your own domain fixes both for a few dollars a year.
The setup is a one-time job: you add a few DNS records (SPF, DKIM, and DMARC) at your domain host that authorize your newsletter tool to send on your domain's behalf. Every serious tool has a step-by-step screen showing exactly which records to paste where, and verifies them afterward. Budget fifteen minutes.
A refinement for the ambitious: use a subdomain (mail.yourbrand.com or news.yourbrand.com) for your newsletter. Your newsletter traffic then builds its own reputation, separate from your regular business email, and an incident on one side cannot damage the other.