I think going with Jet2 and flying straight to Manchester maybe the best option, there is a regular shuttle train from the airport to the city centre (Manchester Piccadilly Train Station) and the meet is based only a short walk from there.

I have just checked the prices and it's around €120, I think that is pretty good. Certainly the easiest option, I am not sure what the public transport links are like at Liverpool Airport.

Cheers

Cris.