I'd suggest that DBISAM, or now probably their newer ElevateDB, should be strongly considered. From your previous experience I expect you know it doesn't add much size to your executable, is reasonably fast, dependable, perfect Delphi-based solution, and has excellent support. Over the years their SQL dialect has been refined so it's now very nice with high degree of ANSI SQL-2003 compliance.
DBISAM/ElevateDB is as you note not open source, but the licensing cost is per developer only (not per deployment) so if there are only a few developers involved the cost is (in my opinion) negligible. Licensing cost is especially reasonable when you consider the level of support and responsiveness you get on DBISAM/Elevatesoft newsgroups, where the main developer/owner (Tim Young) is actively involved answering questions and solving problems. Aside from cost of a proprietary solution, there's of course also concern over whether the business will survive and product will continue to be developed and supported in the future. That's something you have to weigh for yourself, but development seems as strong as ever. They've got .NET providers for their db's, and support cross-platform development with FreePascal/Lazarus.
One plus to DBISAM's fulltext search is that it is tightly integrated into the SQL. That is, you can issue a single SELECT statement that directly combines ordinary WHERE criteria on some fields with fulltext search criteria on others. Depending on your needs, this is a nice feature that makes it really simple and fast to do some things that would take more work using a different fulltext solution. I think most add-on solutions, like Lucene and others that might be used with Firebird, don't integrate as closely with regular SQL and restrict you to retrieving a set of records with fulltext criteria only. Something like Textolution's proprietary add-on for Firebird (http://www.textolution.com/ftsib_example.asp) looks like it could accommodate constructing single complex (nested) query that would apply both regular and fulltext criteria, but DBISAM does it more elegantly. And adding a proprietary add-on to an open source db sort of defeats the purpose of going open source, anyway.
One shortcoming of DBISAM/ElevateDB's fulltext search, I think, is that is supports only use of 'AND' and 'OR' conditions, doesn't have any proximity search.
I notice that there is a fulltext solution for SQLite, http://www.sqlite.org/cvstrac/wiki?p=FullTextIndex. I haven't ever used SQLite, but I know a lot of people love it. One area where I'm pretty sure DBISAM/Elevatesoft has big advantage is in multi-user applications where robust locking functionality is required, though that wouldn't necessarily carry any weight at all for single-user desktop app.
