I Use custom matches as long as you don't use casual mode you will get achievements and it counts towards the leaderboard. Also you can have a match with 1-4 people . As far as public lobbies no I don't really see this happening ,even though it sucks for those that stay in the match since some matches can go on for an hour or better and sometimes stuff happens where people have to leave.
Now let's take another view at it if by chance you get put Into a lobby where the other persons goal is to try and make you rage quit by purposely failing challenges and taking a search boxes and not helping the team at all should you get penalized if you leave.------ twisted logic
i see many reasons why this won't happen while it sucks for those just trying to enjoy the game ,, IDE suggest just getting at least one other person and playing custom on regular or hardcore , but that is your choice .
either way good luck
My only advice is to find some people you get along with and friend them. I will admit my experiences in public lobbies have been pretty solid this year. Met some good guys and by the time Nightfall was full swing, I had a good team to play on the One and the 360. The only issue becomes getting everyone to play at the same time.
Also, don't start game unless everyone has a mic and find out their motive for playing........whether it be earning teeth or going for the achievements.