To get into a MvM server avoid the Co-Op selection on the main menu screen and go to the server browser instead.
Just filter for "mvm", find a server with less than 6 players on it (*always* right click and view info before joining-- the server browser likes to lie) The beginners level is "mvm_Decoy" if you want to start off there to learn.
That way you avoid lines completely, but you may join a server that is part-way into a round. Doesnt really matter as you typically get more loot to start with and upgrade immediately to take on the advanced threat.
Pretty fun so far =) I noticed they just updated as well, so maybe the match finder is smoothed out too.. either way this will get in you in very quick.