How do i do seo keyword research without a big budget?

Keyword Planner is free with a Google Ads account, you don't have to run ads. Without spend it shows volume as ranges, but that's enough to tell 50 from 5,000. Trends for anything seasonal.

Search Console costs nothing and for this it beats most paid tools, because it shows you the queries you're already turning up for on page two. Those are the cheapest wins you will ever get - the page exists, it's just not quite there. Beyond that: type your topic into the search box and read the autocomplete, open the people-also-ask box and keep clicking the ones that expand, and go through the headings on the pages currently ranking. The free tiers of the paid tools hand you volume for a few terms a day, which is plenty when you're choosing between three ideas rather than building a list of five thousand.