Whether buying a stand alone digital recording unit or a computer based recording system, both have their pros and cons.
If you have a PC, especially a newer one, you have the advantage of a large number of tracks to record. You need a decent sound card, ( most computers a least have Sound Blaster or Sound Blaster Live,) that allows you to plug in the cheap microphone that comes with the card or computer.
You can download a free usable demo from of the n-track software from their website. The cool thing about n-track is it's inexpensive, around $40.00 for the fully workable software! For $40 you get the capability of a stereo multitrack digital hardisc recorder!
I have a newer Dell PC with the n-Track software. I also use a small Mackie mixer that I plug into the computer sound card's microphone input. Now I can use decent microphones and other equipment like a drum machine through the mixer to the multitrack recorder on my computer.
There is a learning curve to digital multitrack recording. But it really has revolutionized the way musicians can make music. This stuff for making a quality recording, only 5 or 10 years ago, would cost you the BIG BUCKS in a recording studio. It's great to use it for songwriting or producing a demo.