If you have a low budget, I'm hoping you are at least on Google Search Console and Google Analytics. I've done SEO for $100 million companies for 10 years and have never paid much for rank tracking. In fact, we currently use this report I built in Looker Studio (see the link below).

I personally like this data because it comes from Google. When a URL from your site shows up as a search result, Google records the search term, the URL that showed up in the SERPs, and the rankings.

You can use this link. If you are logged into your Google account, you should be able to select any of your sites. You can apply filters to specify search queries or you can download the data in Excel and analyze from there.

https://lookerstudio.google.com/s/tyqPjiiRw48

Make a copy for yourself and do what you can to make it even better. Looker Studio is an amazing free tool. It's worth the time to learn what it can do.