Which database management system type to choose for price tracking?
I would suggest building a test system using whatever DBMS you're most familiar with.  As speed is a mission-critical requirement, I would put the data on an NVMe SSD, and load it up with as much fake data as you can create, then put that through a rigorous set of tests.

Back-of-the-envelope calculations suggest you'll need around 100 GB of space for a years-worth of data, so a 1 TB NVMe SSD should suffice.  Of course, if data redundancy is a concern, you may want two, with data being mirrored between them.

PostgreSQL should have no difficulty handling your data.