Forum Moderators: open
(...)what DBs work best?
Could you give us your definition of "best" first? :-)
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Now that we've got that out the way, here's my $0.02
Microsoft SQL is a good piece of software with a great set of features. It has a price tag to match. I look after a few servers running MSSQL - usually where the customer is a MS-only shop and they aren't interested in saving $$$/year on licences when they're turning over $,$$$,$$$/year and everything's working just fine.
MySQL isn't always loved by true open-source fans because of its licensing. Depending on whether you have a need to distribute it this might not apply to you.
Compared to MySQL, PostgreSQL is perhaps more "open" in this regard.
If SQLite has the features you need, use it - bear in mind it lacks certain common ones [sqlite.org] though.
I've got several sites of my own powered by MySQL and a new one powered by PostgreSQL. Both are doing just fine. Both are costing me a lot less in licence fees than Microsoft SQL would do.
Like with any other software, I try to pick whatever fits the particular project I'm doing.