In some 300+ G40 games, I’ve never bought a battleship unless the game was already won I could do whatever I wanted.
I can’t remember the last time I bought a battleship in a game. If I am going to spend 20 IPCs on fleet, I consistently purchase a destroyer and a cruiser – this hits on average more often than a battleship, has the possibility of generating two hits on both attack and defense, and might increase the number of units required to successfully attack my fleet (the math on this one is a bit fuzzy since there are so many variables involved in fleet attacks), and gives me an extra unit that I can detach for a separate mission if necessary.
On the other hand, I have purchased AA guns occasionally, when I expect the number of planes attacking to exceed the number of AA shots I currently have available and/or when I need to empty the treasury because I know the capital is going to fall. Other than that, AA guns would be my second least purchased unit.
Tactical bombers are also rare purchases for me, but I do purchase them occasionally (more often than AA guns).