Definitely household. Handheld stuff have outdated graphics (like N64 graphics) and they don't entertain you near as well as household game consoles. And of course, they usually allow GOOD online play.
Household no doubt, psp sucks after a while i have it, nintendo ds will get old, trust me. Get 360 some great games coming out like Modern Warfare 2, itll be sick. There are endless games for household, handhelds are only good for trips.
Fallout 3, Gears of War 2, Call of Duty Modern Warfare/World at War, NBA 2k9, Dead Space
I would think of who the game system is for. If it's just for one person and they spend a lot of time waiting like in cars, buses, office visits then the handheld would be nice. However a household one is nice because of the large screen and it is easier for more than one player.