You won't be able to use any binos over 12 power without a tripod or image stabilization.If it is from a fixed position with a tripod,those Stieners would work great.If the binos are to be used hand held,I would stay with ten pwer or lower.
You can't carry binos with objectives from 40mm on up covertly,if there might be a problem with that,look smaller.
There is a large weight penalty between 42mm and 50mm objectives in all brands,I have decided that the minimal light gathering gains are more than offset by the weight and size losses in the larger binos and see no reason to go above 42mm in portable binos.
If "look at the dude with the binos" is no problem,7X42 offer a good compromise between light gathering and portability,this is my choice for use at night in my line of work.
If you are talking about carrying somthing around with you in a coat pocket,just in case,stick with 25mm or smaller objectives and 10 or less power.
In your price range, you might look at compact binos from Nikon,Bushnell and Pentax for a lot of nice choices.
However,in small binos,ergonomics are even more important than in larger ones ,so,if you can,try before you buy.