Identify who your closest online competitors are, and forget about potential brick and mortar and bigger competing businesses offline.
Don't just look for other website that offer your products and services but instead go wider to find sites where your target persona/audience is likely to be hanging out and spending their time.
Gather 4-5 of these URL's and drop them into SEMRush, use the SE Keyword reports to find the sites with the largest overall footprints and export those lists of terms. Keep this all in an Excel file for now.
You'll then want to build some simple filters to separate and tag the terms that are commercial/show buying intent, and have search volume. The average CPC numbers (the price someone is willing to pay, on average, for Ad clicks from Google is a good leading indicator on the commercial value of the keyword -- but it's only really applicable for paid search.
To get organic search competitiveness dialed in you'll need to enrich this data with additional metrics like links and topic relevance, for which you'll likely want to use Ahrefs or Majestic.
For a much more detailed explanation of the process from soup to nuts check out: