I want to make a password manager that from a single master password generates passwords for my services. For that I thought that HKDF suits my needs, as it is able to generate multiple keys from a single strong key. Here I read that HKDF is secure if the key is "good" which password aren't. So I thought about using PBKDF2 to generate the key to be used with HKDF.
Is this design good?
master_key <- PBKDF2(master_password, ...) service_key <- HKDF-Extract(master_key, ...)
How would I then handle salt? It should be random, so it should be stored somewhere. Can I store it anywhere? Can I use the same salt for the two phases?
EDIT: I think I should add a clarification.
The reason why I would do this is to have a way to have my password wherever I am without the need to have on every single device I am using the database file (I've used keepassx for a while and that was frustrating, because you then need to handle syncing and such). This way the user is required to remember only the master password (and the salt?) and perform the calculations with a specific tool.