Which full-text search package should I use for SQLite3?

As of 3.6.21, FTS3 is well documented, and gained a more officially visible status.

FTS3 is part of the standard sqlite DLL build on Windows, not sure about the amalgamated source.

We've been using it on production for about a year with no particular issues.

I've looked into full-text solutions recently too. It seems like SQLite has no de facto choice right now. No matter what you choose, it's inevitable that you'll have to re-architect it as the various FT2, FT3, etc. solutions mature. So bite the bullet and assume you'll need to do more development in the future to keep pace with changing full-text technology.

Sphinx Search has no direct support for SQLite yet. It supports only MySQL and PostgreSQL right now (ca. August 2009). So you'd have to hack your own SQLite connector or else migrate SQLite data to MySQL or PostgreSQL and then index the data with Sphinx Search. I think someone is working on a Sphinx Search patch to support Firebird, so maybe it's not so hard if you're willing to roll up your sleeves.

Also be aware that Sphinx Search has some limitations about incrementally adding data to the index. You should spend an hour or so reading the doc before you decide to use it.

I don't know of any direct way to index SQLite data in Lucene either. You'd probably have to write your own code to process batches of SQLite data, adding rows to the Lucene index one at a time. This seems to be the usage of Lucene no matter what the database.

update: Solr is a great companion technology for Lucene. Solr gives that search engine many features, including the ability to bulk-load query result data from any JDBC data source.