Step 1: Name the pattern first.
Low blood pressure plus full neck veins plus faint heart sounds is a well known combination called Beck's triad, and in a patient with chest trauma it means the heart is being squeezed by fluid trapped around it, that is, cardiac tamponade.
Step 2: Use the neck veins to sort out the type of shock.
If this patient were simply bleeding out from his injuries, the neck veins would collapse rather than bulge, because there would not be enough blood to fill them. Since the veins are distended instead, the problem is blood struggling to get back into a heart that is being compressed, not a lack of blood volume.
Step 3: Check the lungs before blaming them.
Both lungs are ventilating fine on exam, so a collapsed lung or a large blood collection in the chest cavity is not driving this picture, even with the rib fractures present.
Step 4: Decide what must happen first.
Tamponade kills quickly by stopping the heart from filling, so it has to be drained before anything else. A pericardial tap removes the compressing fluid and lets the heart fill and pump again.
Step 5: See why the other choices wait.
Giving blood does not solve a heart that cannot fill because it is squeezed from outside. Chest tubes are not indicated when air entry is already normal on both sides. The limb with weak pulses does need vascular repair, but a squeezed, failing heart is the more immediate threat and is treated first.
Step 6: Conclude.
$\boxed{\text{Urgent pericardial tap}}$