MCB:
Have no fear with regard to booking with First Choice. They are one of the leading tour operators in the UK and have their own fleet of aircraft.
I have flown with them to Cuba before, also have booked with them before and flown on Thomas Cook Airlines (Cayo Coco).
In fact this up and coming trip to the Playa Pesquero on December 2nd I have booked through Eclipse Direct (the direct selling arm of First Choice) and am flying First Choice Airlines from Manchester.
On their long haul flights they have replaced economy with what they call Star Class on their Boeing 767 aircraft. This includes a fantastic 33” seat pitch, personal seat back 7” widescreen TV monitor, four course meal and snack before landing and complimentary pampering pack and headphones. This is way better than any competetive UK Charter airline.
I have to say though that this is only on their long haul flights and these aircraft would not be the ones flying the route to Greece.
If you are looking at packages why don't you hit the 'Sell Offs' at the top of the page on this site and from the UK Sites try Eclipse Direct and First Choice. One tip - often Eclipse Direct offers the same holiday as First Choice but can be £60 per per person cheaper. It doesn't always offer the same range of hotels, but it definitely is worth checking out.
I never check holidays to Greece, but I have just had a quick glance at both sites and they only show Rhodes for April and Greece itself is not listed, so online booking on their website, at the moment, doesn't seem to be an option as far as I can see.
However you can rest assured First Choice is a reputable company and I will tell you more about them (hopefully all favourable) when I return in December.