I know that the sequence is important. Inversions are usually towards the end of the workout after standing poses and before shavasana.

The classic yoga sequence of twelve major asanas (presumes warm-up with sun-salutes):
headstand
shoulderstand
plow
fish
sitting forward bend
cobra
locust
bow
half-spinal twist
balance posture (tree or crow or..)
standing forward bend
triangle

I believe this sequence is prescribed in Patanjali’s yoga sutras.
Here is some good background to the classic sequence.
And a little more here.

p.s. That sequence is designed for gross and subtle reasons to energize the spine and other nervous centers in that order.
In some some real sense doing asanas in some other sequence that you make up is stretching and not Yoga.
If you are more advanced you can learn oodles of variations and other asanas that work the same muscles and nervous centers. But you would do the same sequence with appropriate substitutions.

I would avoid combining the crouching tiger with the hidden dragon.