Well #1 zombies would not just "spawn in my room" i'd prolly have some warning.
But for arguments sake, lets say they do. I have a 3 foot machete next to my bed that would most likely be my first choice, also i got a 5 foot walking staff in the corner.
and before anyone asks, yes, the machete's purpose for being next to my bed is for zombie attack.
also in terms of surviving, one of my first stops would be hardware store/sporting goods store (assuming that my stash has been taken out) pick up some weapons and high energy density food. then camp out on one of the water towers, reason is, zombies cannot climb ladders (they just don't have the coordination or flexibility in their limbs to do it). only really need to stay there for about a week or so because by that time vigour mortis will set in causing the zombies to be essentially frozen in place.
most of this is optimistic but better that than pessimistic