Yeah your system is DOL-001, you do have a digital out for component, however that cable you listed won't work. The Gamecube's component cable was Japan only and discontinued quickly because of poor sales. They have a processing chip in the plug, which can't be replicated, so if you really want progressive scan, better color and a way sharper image, you're going to have to spend around $160-220 on a used, official cable.
As for games, Metroid Prime, Metroid Prime 2: Echoes, and Killer7 are my first 3 picks, then in no particular order: Animal Crossing, Luigi's Mansion, LOZ Twilight Princess, LOZ Windwaker, Kirby Air Ride, Super Monkey Ball 1 and 2, Super Mario Sunshine, Starfox Adventures, Paper Mario: The Thousand Year Door, and Smash Bros Melee. :P
Gamecube is still the system I play the most, though I do speedrun, and play Prime 1 and 2 casually, which accounts for a large amount of my time spent playing games. :P
Also, do buy a triwing screwdriver, it's likely you'll need to adjust your GC's laser at some point. When you start getting disc read errors (DRE) you'll need to open it up and tighten the trim pot on the laser to adjust its focal length. Dead simple to do, don't be intimidated by opening it up. Just look up some instructions on how to do it.
