The player cares about:

• his owned engineers (water pump, solar panel, etc).
• perks for hire, available cash, and per-round income. Hireable building engineers can be superimposed on the existing building engineers, transforming flat non-clickable pictures into clickable "hire-me" buttons
• his owned non-engineer perks. this perk list can grow very, very long and needs a lot of space. 16+ items is normal in later rounds. Now that players can hire more than one permanent perk per round, 30+ items may start appearing in later rounds.
• details about the available maps for next round
• his opponents' engineers and perks. this is important because the AI has hard counters to the player's strategy half the time. These engineers and perks are relevant in the context of you deciding which map to pick.
• resource prices for next round

I don't think company stock prices should be displayed in the campaign's current form, because stock price ranking compares the player's performance to the AI's. However, the AI's performance is imaginary, since it does not actually play, but receives random bonuses instead. Many players have expressed surprise that the AI is able to do better than the player, but this is misleading.