The body methods are more important than animal forms. They are standards required to some degree in most movements.

In fact, if you just perform the Old Three Steps and the Finishing, you can get a lot of practice with the fundamentals.

In this table, I've highlighted which Body Methods are the easiest to focus on during practice. Just focus on one at a time in the beginning.

Chicken Legs - The foundational characteristic. Power, speed, and control even on only one leg. The first thing you should learn, and the first thing you should practice every session. Different moves will manifest slightly differently (eg Dragon Carries Shoulder Pole has a wider base than Chicken Step), but the characteristics of low, stable, controlled, protecting the groin, quick steps, and quick turns are always there.
Dragon Waist - Flexibility here translates to greater power at the "corners" or extremes = where you might contact an opponent. There are moves in Xinyi that compress, twist and otherwise work with the abdomen. Just learning to swing initially, a la Dragon Carries the Shoulder Pole is good.
Bear Shoulders - Some degree of rounding the back is always present, even standing.  There are some movements that practice the opening and closing of the shoulders, (like the variation of Chicken Step that uses arms with every step, rather than just at the turns). Dragon Carries the Shoulder Pole lets you practice the dropping and "rolling" of the shoulders.
Eagle Claws -  In Li Laoshi's lessons, this was interpreted to mean keeping some curvature in the fingers = not completely straight*. It's good for grabbing, keeping energy in the fingers thus (avoiding some locks). In the Classics there's the saying 把把如鹰抓 ba ba ru yingzhua means every move like Eagle claws. So we can also think of all our moves with the intention like an Eagle snatching prey.
*The fingers may expand slightly on impact, but it's instantaneous.
Tiger Protects the Head - There is a move called "Tiger Protects Head". But as a Body Method, this term refers to keeping everything in nice and tight, arms touching the body when they're not extended. The elbows don't leave the ribs.
Thunder Roar - You make a sudden, sharp, loud sound co-ordinated with movement. It should sound something like "Yee" (噫). In practice, you mostly do this as the last move in the finishing. In use, you can combine a shout with any movement for maximum shock. The Thunder Roar is for relieving tension, projecting power, and shocking the enemy.