Ah mate, listening to it that sounds like really poor interference that is being amplified by the amp simulators.
Have you a link to the cable you bought (Amazon/eBay etc.) to get an idea on what you're actually using?
Have you the budget to get a better audio interface? Need to get it sorted as it sounds like you can play well and don't want to hold youself back using crap like that! ... no offence!
For reference, When you hold the strings your body is being used as ground and that's why it stops some of the buzzing, the gate plugin will then push that into silence. This is a problem that most people have when first recording guitar. I got so annoyed with mine i pulled the guitar apart and re-lined it with shielding tape, and re-wired the pickups, it's incredibly silent now.
If you've got single coil pickups then hum is very hard to get away from - Never owned a single coil guitar though!
What kind of mac are you using? Don't suppose you have one that already has a line-in source?