Well, there are two free options I love. Both Google products. One is Google's Search Console, the other being Google Analytics.
Search Console is great for tracking changes to your site, monitoring your impressions, clicks, & problems Google identifies with your website.
The other option which works well alongside is Google Analytics. The name says it all - it's more data-driven, and it's not restricted to Google search. Furthermore, you could monitor how your website is converting, since X change.
To be honest, I couldn't live without either.