Neoclassical model with proportional taxes
In your household problem you have a typo, they maximize their utility so I think you meant $\sum_{t=0}^\infty\beta^tu(c_t, L_t)$. Now their income comes from the profits of the firm $\pi$ their wages $w_tL_t$ and what they borrow-lend (not directly the production $Y$ or government expenditures $G$) and their expenditures are consumption, paying their debts (or receiving money from what they lend yesterday) and what they pay in taxes. Obviously they only pay consumption taxes, bond taxes, and labor income taxes, since consumers don't directly invest. We usually model that investment decisions are made by firms, so investment taxes will enter the firm's problem. 

In contrast, the social planner chooses everything so all taxes will be relevant for his problem.