Ultimately you're not going to get the best deliverability unless you have access to the DNS records you are sending from, because you won't be able to pass DMARC.

However, you can still pass SPF and DKIM checks by using your own domain, which involves taking advantage of SMTP's envelope sender address. This can get you acceptable deliverability, assuming good IP, non-spammy content, low volume sending, bounce management etc.

There's a pretty good StackExchange answer here that explains the differences between SMTP envelope and message aspects in more detail: https://security.stackexchange.com/questions/30732/why-is-it....

There's also a good MSDN blog post series on the various email authentication techniques and how to get them working: https://blogs.msdn.microsoft.com/tzink/2013/04/24/how-to-set...

The gist: set up an address, and SPF and DKIM on a domain you control, and use that address as the SMTP envelope sender. Then "spoof" the FROM header.

The caveats: this technique is still used by some spammers; some clients will display "From: (your domain email) on behalf of (actual sender)"; some MTAs use SenderID which applies SPF to the FROM header's domain; some (but not most) providers almost need DMARC to get bulk email to the inbox nowadays.