This tune has a beautiful melody. It works great with the cross-picking style. The slow tempo makes it an easy introduction for those who are just getting used to cross-picking. If you are using alternate picking, then closely follow the pick direction markings in the tablature. If you are brand new to cross-picking, you can play this entire tune with all down strokes. Even once you are able to truly "cross-pick" you may still prefer the sound and feel of using all down strokes.
There are other ways to cross-pick in regards to pick direction and some of those options are in the licks. Analyze what you are learning. Notice how so much of the melody uses Arpeggios and notes from the D major scale(Arpeggios are chord notes picked one at a time). Make listening a regular part of practice and warmup with D major scales and scale patterns. If you pan on jamming make sure to work on some basic rhythm playing. You can learn more about rhythm playing in the learning paths. For this tune, focus on playing in "waltz" time. You'll use the boom-chuck-chuck pattern.