It's a matter of choice.
Reinstall is a vague phrase...do you mean a clean install (one where everything currently on the drive is wiped out and a new install of XP is made) or do you mean a repair install (one which replaces all system files but leaves all programs and data files intact)?
A reinstall/recovery/restore set of disks offers one alternative, while an actual MS XP Home CD offers another set of alternatives.
If you are trying to do a repair install
(sounds like it, IMO)...then there are certain rules that come into play. The one you are confronted with is the fact that XP is set up so that the current version installed...cannot be repaired by a version which has an SP-level reflected that is not equal to or greater than than the version installed.
E.g., I have SP3 installed on my systems. I have all sorts of valid, licensed XP Home CDs (some which reflect no SP, some which reflect SP1, some which reflect SP2, some which reflect SP3. I can only use the CDs reflecting SP3 to do a repair install on my current system...because it reflects SP3. If the system reflected only SP2 or SP1...I could use any CD for XP Home which includes either SP2 or SP3.
The smart (IMO) way of overcoming this is to create a new XP install CD, a process called slipstreaming.
Slipstreaming Windows XP To Create a Bootable Windows XP CD or DVD - http://www.bleepingcomputer.com/tutorials/slipstreaming-windows-xp-to-create-bootable-cd/
There are many guides on the Internet which describe how to create an updated/slipstreamed XP install CD...the result will be the same, but the steps taken will vary depending on the thought processes of the author.
IMO, the easiest way to create a slipstreamed XP install CD...is to use the nLite tool.
nLite - Deployment Tool for Unattended Windows - Guide - http://www.nliteos.com/guide/index.html
The other alternative is, of course, to request copies from the system manufacturer...of restore/recovery CDs.
If the intent is to do a clean install, you can just use the XP Home CD as is. But the first step should be to just delete any existing install partition that currently exists, using the XP CD.
How to Perform a Windows XP Repair Install - http://www.michaelstevenstech.com/XPrepairinstall.htm
XP Clean Install - http://www.michaelstevenstech.com/cleanxpinstall.html