What is the ideal database that allows fast cosine distance?
If it's only a few thousand entries each with a 1,000 features, you may just be able to keep it in RAM if you are running this on some kind of server. Then when you get a new feature vector, just run cosine similarity routine. An easy way to do this is just use something standard like pandas and scikit-learn.

Alternatively you can keep everything in SQL, load it into something like pandas and use scikit-learn.

I'm actually not sure you'll get much of a speed up, if any, by writing the computation in SQL itself.