In a nutshell, the version that works on your hardware and runs the software you want to use!
x86 and SPARC are 2 completely different hardware architectures.
In very simple terms, the x86 architecture is based on, and has evolved from, the original IBM PC of 1981. x86 is a generic term used to refer to anything based on Intel 16-bit and 32-bit microprocessors. Your Pentium III is a 32-bit Intel microprocessor. Therefore, you will need to download and install the x86 variant of Solaris.
As for SPARC, visit this Wikipedia link for a very good overview:
http://en.wikipedia.org/wiki/SPARC
But let's get back to basics. Why are you interested in running Solaris on your Pentium III PC?
Solaris 10 is the latest and greatest version of Solaris, but if the software you want to use is only supported on Solaris 9, then that's the version you want to install and run.
When a software company (vendor) says that their software is "supported" on Solaris 10 or 9 or whatever version of Solaris, they mean much more than just saying they provide technical support. "Supported on Solaris X" usually means that the vendor has thoroughly tested and certified that their product runs correctly on that particular version of the Solaris operating system.
Installing a newer version than is "supported" is a risk. The vendor's software may not have been tested on that version yet, or may be in the process of going thru testing but not yet been certified. Whether or not the software runs on the newer version is a risk you take on your own. It may work just fine, but if it doesn't, you'll be back-pedaling to installing the correct version of the operating system and re-installing the software.
So, first thing is to know what software you want to use. Then, get the version of the operating system it was made to run on.
John