AoB is very, very difficult on anything other than Medium (where it is pretty easy). Even after you get the chainsaw there are a lot of tough enemies early in the game. I have not successfully won an AoB Hard or UV game yet, although I have gotten pretty far in a couple Hard games.
But you are basically correct, you run on coward mode until Dlvl 3, where you start searching the level for the Chained Court stairs. If you are lucky, you find them quickly and don't use up all your healing. Then you hope that you get some relatively easy levels with lots of healing and armor until you can make ~clevel 4 so you have a couple levels of Berserk (the extra speed REALLY helps). The difficulty is that I am ususally so low on health that I have to take some Ironman and that means another level before I get Berserk.
Once you get to clevel ~6 so you have Brute 2+, Berserk 2+, and perhaps some Ironman or Hellrunner then it becomes more of a normal AoB game, but there are still plenty of things that can kill you even when you are being careful.