Binoculars have been a lifelong interest for me.
It would be innapropriate to give a tutorial here about how they work. Many of the other posters have touched on some of the key points and given good info.
I believe you stated that compactness and light weight were important and performance in low light was only a small factor. Therefore, I would recommend either an 8X20 or 10X25 binocular. Both have 2&1/2 mm exit pupils which is about the same size as most people's eye pupils on a sunny day.
These are the lightest and smallest with 8X20 holding top honors. 10X25 is still light and compact but with 20 percent more magnification. That means hand tremor (which is not normally noticeable) will be magnified also.
Taking a guess from your post, you will usually not be using your binocs for any prolonged and continuous viewing. So, if your hand is pretty steady, I would recommend the 10X25s.
Which brand to choose is subjective but only down to a certain point in diminishing quality. Generally, the better makers make either 8X20s or 10X25s smaller but not necessarily lighter weight than the lesser brands. Not only that but the better ones will usually be weather proof, more durable and give a much clearer, brighter view in any magnification or lens diameter.
I recommend spending the money and getting Zeiss, Leica, Swarovski. They are among the best. Steiner, in my opinion is a notch down but still excellent. I would trust Nikon's top models and Pentax is supposed to give a good bang for buck. I would also trust Cabela's.
I agree totally with everyone who said that with binocs, you generally get what you pay for.
Roof prism binocs will be the lightest and most compact.