Choosing between the two shades of Munich malts, it's always Munich II by default, if isn't stated otherwise in the recipe. The lighter "I" is a relatively recent invention for creating modern beers, while the darker "II" is the standard malt for traditional recipes.
For this particular beer you might use the "I" as well, as it's a modern style. I'd stick with Munich II however,.
If you are interested specifically in Schwabian beers, the book Bier Selbst Gebraut by Klaus Kling contains two recipes from that region: a Schwabian Schwarzbier and a Schwabian Export Helles. The latter might be of interest to you as is stands stylewise pretty close to a Festbier (just somewhat lower ABV).
The example beer you're linking looks almost perfect. Just almost, because their choise of hops looks questionable: why do they have to use those roughish Perle and Herkules when they might use the classic Mittelfrueh or Tettnanger which impart much nobler character to the beer? I believe, the only reason is the big-industry economical considerations, which are of no significance whatsoever for a homebrewer.
Festbier (specifically the modern German version of it, as you might find also a lot of wildly different recipes called "Festbiers" too) is a perfect style to start your Lager endeavour with. It's simple, nicely filling, incredibly tasty (one of my favourite styles too), and its higher gravity perfectly masks insignificant fermentation or lagering imperfections which are unavoidable at this stage. Brew it, you'll like it!
I'd start with 15% of Munich II and 85% Pilsner. Aim for circa 25 IBU with Hallertauer Mittelfrueh, 1st charge at First Wort Hopping, second charge (half as much as the 1st charge) at 30'. No late hopping.
Schmitz decoction seems to be the ideal option for mashing but if you don't want to fiddle with decoctions yet, go the way of two-stepped Hochkurz infusion, 45' at 63C/145F + 45' at 68C/154F.