Well not an easy task your are asking, since not all ac powered devices like it if voltage is not exactly sine wave... I would recomend buy cheap ready made unit. Much safer too if you dont have experience dealing with ac circuits.
In my country i can get small inverter as cheap as 30 - 50 euros, witch in my standards is cheap... Not much point building one unless your doing it to learn or just dont have any other choise...
Emergency power really docent need much, charge your phone, some led lights going... Anything power hungry you are usually better of getting yourself real generator anyways...