Stansted vs Heathrow

" Looks like about $75 for train from Stansted to Liverpoool Station"

Don't ask for tickets to "Liverpool station" or you could end up 200 miles from London, Liverpool Street station is the one you want.

Where are you going in London? Looks like the train from Stansted to Liverpool Station takes 47 minutes; tube from Heathrow T5 to Piccadilly Circus takes 49 minutes. Less if you are not going that far. So which is more convenient depends on where your hotel is.

The train would be more comfortable, especially with luggage.

As for cost, the tube fare would be £24 (£6 per person) if you pay cash; less if you have four Oyster cards ( between £3.10-£5 depending on time of day). Any way you figure it, it is more than $10 for four people.

You can get a bus from Stansted to Central London (variety of spots) in 60 minutes for 10 GBP/p walkup or 6GBP/p booked in advance.
http://www.nationalexpress.com/cheap-coach-tickets.aspx

Sorry, I didn't type that right, I did check rates to Liverpool street station. Also, the fares for the tube were based on 2 of us being kids/teens and it will be on a weekend so the fares were slightly lower.

From what you're saying it sounds like it's not a bad idea to use Stansted? Our location is London is still TBD, so I can accomodate as needed. (We leave 3 days later from Heathrow.)

I had not tried EuroWings, but it looks like it's the exact same flights as Lufthansa and the same fares. Thanks for the tip, though.

The rail fare can be as little as £8 if you book in advance from the Stansted Express website.