Not sure if you’re hosting on AWS (if yes, free for the first 62k/month), else the $0.10/1k/month shouldn’t be too bad - https://aws.amazon.com/ses/pricing/

From my past experience with Sendgrid, it is trash, most of their shared IPs have poor reputation anyways, had lots of issues with them.

Running your own email server might be a good learning experience, a quick search brought up this all-in-one container solution - https://mailu.io/2.0/

Messing about with Postfix directly could be a painful experience, but yet another possibility.

Either way, new IPs will probably take some time to warm up, so don’t expect full deliverability for the first few days/weeks.

You should check that your cloud provider doesn’t block outgoing smtp traffic - iirc digital ocean and GCP do block.