You can use PostgreSQL, which is free and widely used at the enterprise level, to store stock quotes. However, you will need a substantial amount of money to cover the storage space required for all this data. Take that into account, how much you will have to spend on a recurrent basis to maintain your system.
When hiring a programmer, you need to be specific. This means that if you request a database, you will receive just the database, without a user interface to retrieve data from it, forms, or spreadsheets – only the database and the synchronization tool. Among other details, you will need to provide the type and frequency of data (tick, ohlc, h1, d1???), for instance.
If you require anything beyond a database being fed with data from your API, you will need to provide an explanation, otherwise you will receive only the db.
In my humble opinion, $2,000 is quite low for an IT project; it's equivalent to 2-5 days of work for a professional engineer. Your project, however, might take a minimum of 2-3 weeks, which translates to a minimum cost of approximately $10,000 for a reputable IT company.
You may want to explore websites where you can request estimates, such as Freelancer or others, as you may receive cheaper quotes that align with your budget and expected outcomes. There you will find individuals willing to work for lower fees that will send you proposals.
A tip about PostgresSQL. In case someone recommends you using the PostgreSQL extension Timescale (specific for indexing date-time based records), you should be aware that it is a nightmare for maintaining it as it creates hypertables that hide the actual data layer, generating a lot of drama and pain for the IT teams.
Cheers.