Picking up from Stansted airport at 1am. What's the simplest/easiest/cheapest option?

[HotHotter]

I don't want to have them getting the shuttle bus as they will be tired.

Can you pickup at the 'set down ' location which is £7 but only gives you 15 minutes?
Short stay car park is £13 if less than 30 minutes I believe.

Any thoughts/suggestions?

Haven't used the options you suggested, but you can park at nearby petrol station for 30 mins free (also easily use their toilets if you're travelling a long way), then move car to mid stay for up to an hour free. That way you can be closeby when you're needed.

Yes you can pick up from the set down location. You can wait in the medium stay car park and get them to call/ text as they’re coming out. Or they can hop on a shuttle bus to the medium stay and then it won’t cost anything.

Just to warn you that the express pick up/drop off is now £10 for 15 mins. Lots of people park up near Takely and wait for the family member to call when they're through customs