Park in the LONG-TERM car park (because it's free for up to 2 hours).
Then EITHER
(a) take the free shuttle bus to the terminal, meet your relatives and then take the bus back again ; OR
(b) possibly better, given the mobility problems you mention, arrange for your relatives to phone you on arrival, so that you can use the express pick up almost outside the terminal. (£3 for 10 minutes).
I pick up friends quite often from Stansted and, along with loads of other people doing the same thing, I always use one of those two methods (although it's actually the mid-term car park at Stansted which offers free/cheap parking for 1 or 2 hours). It allows for flight delays. (The short-term car park at Luton charges £7 for 40 minutes. It could work out very expensive if there was a delay to the flight).