Where to pick up a rental car - airport vs. train station

Yes, you pay more at airports, but you also get a larger pool of cars to choose from and better opening hours. There is nowhere near Heathrow or Stansted airport (there is a Stansted village, population 6000!) which will have anywhere near the choice or opening times.
The only place you can get to by train from Heathrow is central London (Paddington station), and you don't want to pick up a car there.
Where is your first nights stay from Heathrow? I would suggest getting a train there, and picking up a car when you leave that place.

For Stansted, the trains to London go via Bishop's Stortford to London, but there is also an hourly train north to Cambridge, which is an option. I would suggest dropping your car of at the last overnight place before your departure (Cambridge?), and taking the train the following day from there to Stansted.

Note: spelling is Stansted.

Seems to be a signification difference in price picking up at train
station

Is there? I'm surprised at that - but if that's what you found - which train station is cheaper? And where are you driving with your car so we can see the bigger picture, because picking up at Heathrow and dropping off at Stansted would be far the most straightforward.

Marisa, Where are planning on driving to ? You could take a bus to Reading from Heathrow and rent your car there and say drop if off in Harlow and take a taxi to Stansted airport. One other thing to keep in mind is that some car rental agencies charge a drop fee when you don't return the car to where you rented it.

I considered goofing around with getting away from airports to save the airport surcharge (usually just charged at pickup at airport, not drop off) but with 5 people was too inconvenient. Drop charges are hefty now, $80 or so. But as noted above, if you want a larger car or an automatic, those are guaranteed to be available at airports. Probably worth the convenience to just pay it.