I'm not sure about the laws in your neck of the woods but if you do record your calls you'll have to let the other party know your doing so. something like "I'm recording this call for my records" or something like that.
Well thats how it is in England anyways.
I think thats why a lot of companies say they are recording the calls for marketing or security purposes.
The OP already mentioned they are aware of their local laws. Here in Canada, you can record any conversation as long as one party (you) is aware of the recording. What that means in practice, a third party can't record your conversation without either of you knowing (*without a warrant).
Anyway, a couple of years ago, my ex-wife had a unique recording on her voice-mail, a TV journalist (well known in Canada) sang her 'Happy Birthday'. She'd kept saving it on her voice-mail every week for several years, not knowing how to save it off of her voice-mail.
Like other posters here, I could remember back in the mid-90's making phone calls through my modem and computer mic/speakers, but I couldn't remember how. I pulled a few old modems out of my box of junk in the closet and got them working, but I couldn't find a way to place a call in XP.
I asked all my geek friends and they all could remember doing it, but none of us could remember what software we used. A google search finally found some old shareware software that I go working after a dozen tries in XP.
Willowphone was the only thing I could find that worked for this.
So for the OP, what you want to do is either use Willowphone to answer your phone through the modem, and then just use any sound recorder to record what's coming out of your speakers, or you can answer on a separate line, then pick up the call with Willowphone as an extension line.