You have literally _tons_ of options for database server. It really depends on your use case and budget.
We'll assume basic relational setup and not object oriented or data warehousing...
Simple and basic use: Any workstation running SQLite.
A step up: MS Access (has a GUI interface for helping the design, creating forms and reports)
Enterprise class, but still usable at lower class level: MySQL, PostgreSQL, and the like (which are free). For extensive support and class A reliability, Oracle, DB2, Microsoft SQL Server, Informix, etc. (which are far from free).
As for hardware, you never really have to worry about it for small projects.
- You do, however, need to make sure your entire DBMS and data store is backed up. This gives you snapshots of the past and also the obvious benefit of restoring if your server crashes.
- For high reliability and performance, a RAID 5 disk setup is nearly optimal for all files. Oracle takes this one step further by suggesting the OS and system files/programs sit on a RAID 1 (mirror) setup, RAID 1 or RAID 10 for log files (mirror and striping with mirror respectively), and RAID 5 or RAID 10 for the DBMS and data. Again, this is for large scale database use (like for an ERP system). For a simple database system, a plain workstation set up with no RAID or simple RAID 1 would work.
- RAM is relatively inexpensive, so there's no excuse not to beef up on it.
- Though hard drives seem inexpensive, quality and quantity should be the focus, with read/write speed, bus speed, and number of drives being more important than disk space per drive.
So, the real answer is, as in many things, with the lack of info about your use case (how many people, how many transactions, what type of transactions -- predominantly read or write?, network setup), it depends. You mentioned "as soon as possible". You can always upgrade, so starting with a basic workstation and an OS you are familiar with is the way to begin.