If Beast Below is played and chooses Vex Ampathic on a battlefield, and that resolves, would the Beast Below be stunned and unable to move?

Yes, Beast Below will be stunned and unable to move for the turn.

Reasoning

1. Playing the Unit: When you play Beast Below, it enters the battlefield. This action triggers Vex, Apathetic's ability: "When an opponent plays a unit while I'm at a battlefield, [Stun] it. They can't move it this turn."
2. Chain Placement:
   • Beast Below has a "When you play me" ability ("return another friendly unit and an enemy unit to their owners' hands"). This is a triggered ability that is placed on the chain after Beast Below enters the board.
   • Vex, Apathetic’s ability also triggers when Beast Below is played and is placed on the chain.
   • Per the rules of simultaneous triggers (Rule 383.3.d), if both players have triggers to place on the chain, they follow turn order. Regardless of the order they are placed, the chain resolves Last-In, First-Out (LIFO).
3. Resolution:
   • If Vex's ability is on top of the chain, it resolves first. Beast Below is immediately stunned and gains the "cannot move" restriction.
   • Even if Beast Below's ability resolves first (returning units to hand), Beast Below remains on the board at the battlefield and is still subject to Vex's stun effect when it resolves.
4. Stun Mechanics: Once Beast Below is stunned by Vex, it cannot contribute its might to damage in combat (Rule 423.1.b) and it carries the "cannot move" restriction for the remainder of the turn. Note that Beast Below remains on the battlefield; it does not return to the base simply for becoming stunned.

This is my interpretation based on the standard chain rules and triggered ability priority. No official FAQ exists for this specific interaction, but it follows the established mechanics for Vex, Apathetic (see FAQ #9240 and #8772).