Soo... If I wanted new tires, but not new rims (I really like the Austin's), I've been looking at getting the Michelin Pilot Sport AS3's in the same size as the stock tires... Do I need to do anything special other than get them mounted to the stock rims??
Oh, and I'm also noob. If you can't tell.
Not at all. Being the same size, there is no figuring if they will work. It's only when the inside diameter changes (wheel size) or when the outside diameter or width of the tire changes significantly. You'll find the outside diameter and width of tires vary up to a 1/4" or so between manufacturers.
Any more than this usual variance between manufacturers, you need to evaluate whether your wheel is wide enough to support extra width and/or your fenders will clear the tire, especially when you hit a big dip in the road.
https://en.wikipedia.org/wiki/Plus_sizing