Lots of good advice here already - so I figure I'd join in with a few things.
Geekgirl brought up the recommendation to add more memory - I think this is absolutely crucial to having the machine operate at an acceptable speed. XP can crawl slower than a 386 running Windows 3.1 if it only has 128mb -- expecially after Service Pack 2 is installed (which is another critical necessity - make sure to update the system at Windows Update after the install). 512mb is a very good target, and most motherboards still in operation can handle that amount. If you aren't certain what type the motherboard needs, an easy way to find out is the Crucial Memory tool - http://www.crucial.com
--- enter your make/model #, and it will tell you the memory type, maximum size module allowed, and maximum total memory allowed.
If the processor is 500mhz or greater, you should be OK.
You mention adding another hard drive? If the drive is greater than 137gb, you might indeed need to check if there is a Bios update that supports the larger drives (the newer 48-bit LBA ["Logical Block Addressing"] support is necessary for >137gb). If this older computer is a major-brand, it's possible that the power supply it shipped with is only strong enough to match well with the original number of drives [ie, you might have a 240watt supply, and two hard drives, plus your other components, might be too much for it]. Look on the power supply's sticker: if it's 300 watts or greater, you should be OK with two hard drives. It it's less than 300 watts, you'd probably want to remove the older drive, and just use the newer as a single drive.
Installation CDs -- make sure to use a retail XP installation CD. Many OEM CDs are tied to the hardware they shipped with. Recovery disks will not work with any system other than those models supported by the manufacturer.
Clean install -- you can do a clean install of XP, even from an XP "Upgrade" installation CD. You simply insert your older-version Windows CD when prompted, during Windows XP Setup.
Bios Battery -- if the system is close to, or past, it's seventh 'birthday' -- the CMOS battery on the motherboard might be starting to get a bit weak. Watch to see if the Bios settings are staying put, especially the time/date. If things are suddenly 1980 or 1990 again, it's time to replace the battery. [Most are 3v coin batteries, and only cost about $1.50].
Protecting Older Systems -- If the processor is under 1ghz, it might be a good idea to go with less-resource-hungry firewall/anti-malware programs, and watch that the auto-start program list doesn't get out of hand [try to keep the processes list in Task Manager to less than forty]. I find that AVG is a good antivirus for older systems, and Sunbelt/Kerio Personal Firewall seems slightly easier on older systems too. Both have free-for-personal-use versions.
That's my two cents - (OK, maybe two dollars, adjusted for inflation)
Best of luck
. . . Gary