Most people who do this use emulators and something like Camtasia screen recording software. If you really want to record your Amiga's output might I suggest an Indivision on the Amiga and a video capture card with HD15 input on the PC? They're a bit pricey, but should give fantastic quality. Need to run the audio separately. For your A1200 if you have Indivision Mk2 you can use Kipper2K's Amiga HDMI cable, here:
http://kipper2k.com/amigaforsale/