I prefer running Oracle on Unix. Oracle is first created on a Unix platform. Unix servers also have a reputation for performing well and for high availability. The price tag for a good, high-end Unix server is not cheap though. And in addition to the DBA, you also need a good sysadmin to support your Unix server.
Oracle on Windows used to perform much more poorly, but Oracle has gotten their product to work well on Windows in more recent versions. And since Windows 2000, the Windows OS has become much more stable than it used to be. You can also get a good Windows server for a very reasonable price. Windows is also easier to administer than a Unix server, for the most part.
Oracle Corp has spent a lot of money and effort on Oracle on Linux. Oracle on Linux has become fashionable lately. You can get a relatively inexpensive Intel platform to run your Linux OS and throw Oracle on there. The only point I'd mention is to make sure that you use SCSI drives instead of IDE drives. IDE drives won't scale nearly as well as SCSI drives should your database require the high I/O throughput. Many companies are moving to Oracle on Linux to keep costs down (like Windows), but yet get good performance and good stability (like Unix).
Keep in mind that the above are just some guidelines. There are exceptions to every one of those rules.