Why does your website need a database? If you plan on having a boring website that never changes then don't waste your time picking or designing a database. But if you want a dynamic website that always changes you really need a data-drive or database-driven website.

The database itself probably won't matter unless you are a hundred-million dollar company with a critical website having more than 1 million unique visitors a day, but even then the database choice probably doesn't matter, depending on your website purposes and implementation. Whether you choose MySQL on a Linux or even Windows-based server or whether you choose SQL Server on a Windows PC web server, it'll likely make no difference. Both MySQL and SQL server are extremely scalable and have an insane potential to handle and process data.

The limiting factor isn't the database system itself but rather the database design. You might not need to hire a specialized database administrator and/or designer to get your site up and running; you just need to have the database programmed efficiently and with some basic fundamentals. The database design shouldn't be redundant and should be designed with growth in mind. Think of possible features you may want to add later and how this would effect the current database. Plan it in a way where it's easy to add tables later or even just add data alone to the database allowing for the site to grow.

Database design and management is usually is a quick process. You can do this pretty fast using phpMyAdmin or an SQL database admin tool such as Navicat. However, even though it is a quick process, you should give it some thought and perhaps even have someone else look at your database design and give you some feedback on the overall structure. Remember, the database is at the foundation and core of your website. Putting yourself in a position where you will need to re-design it will be very costly and difficult later on, requiring you to re-write a great deal of website code (php, asp, HTML, etc) so be smart and design a solid database from the start.