Multi-tenant architecture is definitely a must for SaaS based products/companies. Unless an on premise solution is required, but even then you can use the same code/architecture.
It basically just allows you to store information in databases, based on each specific customer instead of insanely large tables. This way, if anything should require upgrading/changing you can do it on a per customer basis. This is good because if you are a SaaS product then you should most definitely have a tiered pricing structure which will compliment this architecture.
There are a couple different ways of doing multi-tenant but a simple google will show you the differences. Finally, personally I'd go for MySQL, just because I already know it but choosing between the two, or any DB, is almost arbitrary.