Hi, to use the SMTP you need an SMTP service. Your provider has this service if it provides event the mailboxes for your domain, or it can be bought from Mailgun, Mailjet, Sendgrid, and so on.
About the speed, probably even the SMTP service of your provider performs better than the “native” email capability provided with the simple hosting, you should just try.
To use an SMTP, install an SMTP plugin, like wp mail SMTP: it is more flexible than our SMTP addon, and ALL emails sent by your site are delivered via the configured SMTP.
I had the same problem, and I just finished solving it! I needed to an SMTP service, and installed the WP Mail SMTP plugin. In their set up, they give you options (SendLayer, Mailgun, Mailjet, Sendgrid, etc). Instead of another external service, I contacted my webhost provider – SiteGround – and they helped me set up my SMTP record and events through them. It’s included with my web hosting fees. I don’t know what provider you use, but they might help you set up SMTP.