I am creating a server for home use and/or small business. The mainboard can utilize 2 Pentium III 500MHz processors and up to 4 Gigabytes RAM. Will 2 Pentium III 500MHz processors meet the Server 8 R2 minimum system requirement for a 1 GHz processor?

Well, theres two problems. The first problem is that Server 2008 R2 is a 64-bit only release of Windows. Therefor your 32 bit Pentium III's will not be able to run Server 2008 R2 unfortunately. The second problem is that Server 2008 R2 actually requires a 1.4GHz processor, and neither of your processors are up to spec with this.