There is lots of good advice here, especially @TheBigBoy's laconic input. So you want all of the ICE and assets in the trash.
In general, when you play any ID that gives credits per turn, you should use those credits every turn, so trash any unguarded assets.
As everyone here has said, you want to trash all of the corp's ICE, paying as few times as possible to do so. The first step to this is getting all of that ICE face-up. This is a hugely important skill as credits the corp spends rezzing ICE cannot be spent on advancing their game (with the narrow exception of Blue Sun). You want to run a lot early to force ICE rezzes, probably before you find/install Faust.
These early runs may net an agenda, but what is more important is learning what ICE the corp is playing to evaluate how dangerous face-checks may be, how important credit levels are, and how the corp may be trying to win (e.g. Biotic to close the game on a Fast Advance play). You need this information to guide the rest of your game. Gathering and using this information is the biggest difference I see between intermediate level players and elite players.