Pico projectors simply will not cut it in lit rooms. Low lumens + bright room = dim or no image. For a normally lit room you'd need at least a 2,000 lumen projector. Pico projectors are really just novelty items for now.
EDIT:
Instead, I would go with a portable projector:
Top 10 Portable Projectors
May not be in the same price range as a pico projector but these will perform better in bright rooms... and these days projectors are cheap(er) than they used to be.
The hours you won't really notice for a long long time (unless yours are on 24/7). I've got a couple of projectors that are on at least 12 hours a day and have racked up over 2500 hours each (most are rated for 2000 hours) and they're all still going strong (I do have new bulbs in hand just in case).
EDIT 2:
If you are adamant about getting a pico projector:
Projection Calculator Pro - Projector to Screen Distance
Pretty self explanatory, input the make and model of your projector and it'll give you throw distances, brightness, screen size etc.