I have not used Linux before, but would like to experiment with it. I have an HP computer with XP Home on it. Would it be possible to install Linux on my external hard drive [currently designated as drive J] along with some apps suitable for Linux and use it the same way I use drive C on my main computer?

Would it be possible to install Linux on my external hard drive

yes but is tricky for a new user of linux who is used to windows.

[currently designated as drive J]

Linux does not label hardrives as letters like windows does. Linux will use (for a external Hardrive) something like sdb or sdc

Read up on

Ubuntu Full installation to an external USB Hard drive | USB Pen Drive Linux

https://wiki.ubuntu.com/LiveUsbPendrivePersistent

Good luck with it. I boot up my Asus EEE PC Netbook off external SD flash drive so anything is possible.