The simpler the better. Anything you don't have to hassle much with will be apt to get you doing it more. Maybe you already have something on hand like a phone or tablet that takes recordings? I usually use a zoom Q3 video camera. I bet you'll get lots of good suggestions from others on this too.
If you just want to do sound, probably a cheap mic is all you need. Most computers will have basic recording software installed. A windows machine (though I don't have the newer version) should have "Sound Recorder" in the "Accessories" section. You can get a USB mic or some computers may have a small audio input jack. With Sound Recorder, you just click a button to start recording and click a button to stop. Couldn't be easier.
For video, as Marcy alluded to, most cameras (not to mention phones and darn near everythig else) can record you. People sometimes don't even know that their cheap digital still cameras can do video.
I've only filmed myself once or twice, using my phone. The sound quality was pretty bad, but I honestly couldn't say if that was indicative of my lack of playing skill, the room acoustics, or something inherent with the phone (such as auto level recording balance or normalising).
I guess you should try the cheapest options first, then escalate the tech as you see fit...