Nobody wants any stress when arriving back by plane, as Sod's law says something will go wrong.
If there's a Manchester train at 2140, that sounds like a much better option assuming there's some way to get to Liverpool from when you arrive there? Then you can relax.
Otherwise there's the hotel option, but there's no reason to necessarily stay in a hotel near the airport (which will likely cost a fortune). You could look at the Premier Inn website, or Travelodge etc, and find a cheap hotel then simply make for that when you arrive - ideally something that will then enable you a nice relaxed journey to Euston in the morning. Or even look for a Premier Inn or similar in Manchester and continue your journey to Liverpool in the morning?
If there's no onward train after you arrive in Manchester, could you not continue your trip the next day for no extra money (before midday)?
If there's a Manchester train at 2140, that sounds like a much better option assuming there's some way to get to Liverpool from when you arrive there? Then you can relax.
Otherwise there's the hotel option, but there's no reason to necessarily stay in a hotel near the airport (which will likely cost a fortune). You could look at the Premier Inn website, or Travelodge etc, and find a cheap hotel then simply make for that when you arrive - ideally something that will then enable you a nice relaxed journey to Euston in the morning. Or even look for a Premier Inn or similar in Manchester and continue your journey to Liverpool in the morning?
If there's no onward train after you arrive in Manchester, could you not continue your trip the next day for no extra money (before midday)?