I think PostgresSQL n MySQL are in majority competible. And database can be migrated via import / export SQL files from obe to another, 2 ways, @any time.
To bebin to run a forum you need not worry nor learn too much of these. There are hosting packages with all in one services offered to you cheap. Setup are script automated. One click setup basically. Just pay only.
Badically within a day or half day, you can purchase a domain name and begin a forum al lsetup working and only $100~200 US$ charged to yr credit card. There is less than $50 monthly fees, all hosted and backed up in data centers.
Your forum database can be either inside PostgresSQL or mySQL, can be migrated between both, and both are available in hosting data center. They are fully maintained and backed up and kept running 24hr with redundency - quite fail-proof.
Unless u preferred to learn and play w servers, you can just pay n use them without much knowledge.