YMMV. I'm on my 8th day and no word from Xbox360Acheiver.com yet.
I managed to extend the free period by going to "cancel" through the website. Did it a bunch of times to see how low they'd go - they threw in 7 free days twice, and then knocked 33% off the price, which is still ridiculous...
I love XBL because it lets me do something fun, active and social with friends I've made thousands of miles away that I may never get to see in real life.
The options for what you want really depend on your setup.
If your monitor can accept accept component input, you can use the HD AV cables; use the components for the monitor, and use the composite (single yellow) for capturing video to your PC - you'll need either a video card or a specialised...