Index what seems the most logical (that should hopefully be obvious, for example, a customer ID column in the CUSTOMERS table).
Then run your application and collect statistics periodically to see how the database is performing. RUNSTATS on DB2 is one example, I would hope MySQL has a similar tool.
When you find some oft-run queries doing full table scans (or taking too long for other reasons), then, and only then, should you add more indexes. It does little good to optimise a once-a-month-run-at-midnight query so it can finish at 12:05 instead of 12:07. However, it's a huge improvement to reduce a customer-facing query from 5 seconds down to 2 seconds (that's still too slow, customer-facing queries should be sub-second if possible).
More indexes tend to slow down inserts and speed up queries. So it's always a balancing act. That's why you only add indexes in specific response to a problem. Anything else is premature optimization and should be avoided.
In addition, revisit the indexes you already have periodically to see if they're still needed. It may be that the queries that caused you to add those indexes are no longer run often enough to warrant it.
To be honest, I don't believe indexing three columns on a table will cause you to suffer unless you plan on storing really huge numbers of rows :-) - indexing is pretty efficient.
https://stackoverflow.com/questions/418744/what-is-the-cost-of-indexing-multiple-db-columns