I feel like I get reach-outs a lot from early-stage startups, so discoverability isn't so hard there, but I'm a little too risk-averse to take them on -- I'd prefer something with slightly more stability. It seems like I need to do some research to find those.
Is there a good site or database for this?
Check out startup databases. There are several databases that track startups and provide information about their funding, team, and products. Some popular ones include Crunchbase, AngelList, and CB Insights. These platforms allow you to search for startups based on various criteria such as industry, funding stage, and location.
Attend industry events and conferences. Industry events and conferences are great places to meet founders and employees of mid-stage startups. You can network with them and learn more about their company culture and opportunities. Some popular events and conferences for startups include TechCrunch Disrupt, Startup Grind, and Collision.
[1] https://wellfound.com
You may also have some luck browsing the monthly HN job threads to see what's out there.