Clearing out a old secondhand computer is a good idea.
Ideally, they would have given you the installation disks, so you could have reformatted and installed a fresh system OS.
There are many things you can do to continue the cleaning process. Disk Defrag comes later, after you have removed everything you don't need, and installed the essentials, like a firewall, an anti-virus and an anti-spyware. Those last two are needed to do a complete scan of the system to remove any unwanted malicious files, and the firewall is needed before you use the computer on the internet.
You've gone through the Add/Remove Programs in the Control Panel, but likely there are Accounts to be deleted. But make sure you create your own Admin account first. We find that more often than not users do not create their own accounts, and instead use XP's default Administrative account. Not a good idea in case an account profile becomes corrupted. Then they are stuck, and cannot log into XP as an Admin user.
So, if this computer only has the one Admin account, you shouldn't delete it, but instead clean out its My Documents file contents. When you create your own Admin account, the XP System's Administration account will disappear from the login Welcome Screen, but it will still be available in Safe Mode.
Check what is being loaded at Startup in the MSCONFIG editor, (Start > Run, type in msconfig, click OK, then click the Startup tab), and remove any unwanted startup entries.
Check the hardware. You can check the Device Manager, (right click the My Computer icon > Properties > Hardware tab, then the Device Manager), for any exclamation marks, but also, don't forget to open the case and clean out any dust build up, especially on the fans, using a compressed air spray. Check for any blown or bulging capacitors.
Then run an error check on all the hard disks, (CHKDSK), before defragging. The Windows Defragmenter is fine for this, and you don't need to defrag often, although I would on the machine you have, just initially.
The CHKDSK will need a reboot to run and will take hours, depending what size hard disks. Defrag will also take a while.
Make sure all Windows Updates have been installed.
You don't say much about the computer specs but always the best way to get better performance is to add more RAM, unless it already has 1 to 2 GB.
Keep away from harm when surfing. The best way is to use any browser other than IE or IE based, and any other email software than Outlook Express or Outlook.
I hope that helps.