For a budget of ~ $250, you could probably go for a
samsung. (my mom's collegues bought her one for her farewell
gift)
With a higher budget of about $350+ you can get most 6 mp
cameras from brands like Fuji, Canon (power shot, not lxus) and
nikon.
a few things to take note:
Iso settings. (amt of light sensitivity, the higher the iso the
better, that is , in the case for night shorts, though u will see
more noise in your photos)
Lens type. A wide angle lens would be better when zooming in, as
you capture more detail.
Type of card slots. For cameras like olympus, their cameras do
not use Sd card, instead they use XD cards.