Most likely #2 would be the best bet for both hobby level and above. You could do some fun stuff with Postgres and pgvector, but you'll be "limited" to creating some embeddings with an existing model, storing them in pgvector and again using that to add context to an existing model (more or less).

#3 would limit you to running existing models in a browser.

Only #2 would allow you to actually understand and create new meaningful models.