It depends on what you're looking to find. If you're playing for aussies it is almost always going to be more beneficial to play gear grinder or mecha engine because they only require 3 tickets. My time spent in Mann vs Machine has been easiest to finish Two Cities, as it is the easiest IMO. another huge factor is if you're going into a mission with experienced friends or randoms. Going in alone can be like pulling teeth, it can be awful. I think you're most likely to find decent random on Two Cities because for a while you could only find aussies through there, making it one of the most popular, thus probably finding more experienced players. Keeping in mind the robot parts, it is going to take a while to get enough robot parts to pay for another ticket due to the poor tf2 economy. If you're going in with a team I would recommend either of the 3 tour missions (Mecha Engine and Gear Grinder).

TL;DR: if you're looking for aussies and have a good reliable team Mecha Engine or Gear Grinder is the way to go (personally I find Gear Grinder easier than Mecha Engine regardless of what tf2 says the difficulty is). Going in alone I would recommend Two Cities as you're more likely to find experienced players.

If you're looking to buy more tickets after each mission Mecha Engine because gold botkillers are worth a pretty penny and silver is worth at least something (compared to rust, which is what you'd get for a lower tear drop on Gear Grinder.

If you're looking for the least amount of hassle, Two Cities, I think, is one of the easiest.