Well, let's have a look at what other kit you might have.
If you're going to use the recording "just" to see how you sound and how you might need to focus on specific bits of your music then you should be able to do it without spending any cash.
Have you got a mobile? (cellphone) - most of them have the facility to record reminders or personal notes (it's called "Voice Memo" on mine). It won't sound pretty but it may suffice.
Have you got an old radio-cassette? It's more than likely to have a built-in mic. Have you got a tape you can chuck in it? Point it at the amp, hit record, and play your stuff.
An old Dictaphone?
Looking at minimal spend, if you have a CD player and can burn a CD on your laptop, you can drop your backing track onto a CD. Use the CD player to play the backing track. Kathy's laptop has a built-in webcam so she can use it to capture sound; does your's? If so, then hit record on your movie maker software, hit play on the CD player and play your guitar.
If you're looking for higher quality recordings, then I'd suggest taking the amp out of the equation and getting an interface to plug your guitar into which outputs to USB (You can get one of these for Â£80 in the UK). Import the backing track to your recording software, pull on a pair of cans, set the recording software to play back the backing track whilst recording (so you can hear it in the cans), hit record and play.
"Be good at what you can do" - Fingerbanger
"I have always felt that it is better to do what is beautiful than what is 'right'" - Eliot Fisk
Wedding music and guitar lessons in Essex. Listen at: http://www.rollmopmusic.co.uk