Start with what you can undo
The right free tool is one you can leave. Prefer services built on open standards, such as Postgres for data and plain Git for code, so moving later is a migration rather than a rebuild.
The categories that matter
Hosting for the site or app, a database with authentication, transactional email, product analytics and error monitoring. Almost every small project needs exactly these five, and each has at least one provider with a usable free tier.
Resist adding a sixth category until something is actually broken without it. Every extra service is another dashboard, another bill that can appear and another thing to keep in your head.
Know where the free tier ends
Read the limits page for each service once, and write the one number that will bite you first next to its name: requests per month, database size, emails per day. When a project grows, you will know which bill arrives first instead of finding out from an outage.