The most useful all around power and size of binoculars is about 8x30 (which I use to include 8x32). If you are sitting in one place and need to see better in very dim light, an 8x40 (also 8x42) is better. Even 6x30 (and 6x32) is enough for traditional bowhunting except in areas where you want to spot animals a long way off to keep from having to move a lot to see the animals like when you are in the high mountains or on big prairies. There a pair of 10x40 (or 10x42) binos will work better, and a spotting scope is nice to have too. They will save you a lot of riding/walking/climbing.
Good optics don't come cheap. No matter what anyone tells you, $150 won't buy you good quality optics when buying new unless you find some outrageously good sale. It isn't that a pair of $150 binos is bad or won't work, they just don't begin to compare with even mid-range quality binos, much less the top of the line models. Like David (hunt it) says, better to buy a used pair of $300 binos for $150 than than pay $150 for a new pair.
I would try to figure out how to get a nice pair of binos, even if I had to save up another year to get them, rather than buy cheap ones and then realize you pretty much wasted your money and wish you had waited to put it with some more money to buy a good pair. The Burris Signature Select 8x32 and the Leupold Katmai 8x32 are two good semi-compact binos that sometimes go on sale for less than $250 for the Burris and less than $300 for the Leupold. I like these models because they are smaller than the normal sized 8x30 (or 8x32) binos, are solidly constructed, have good glass and coatings, will last for as long as you do, and have good repair or replacement warranties. The Leupolds cost more but overall may be the better pair of binos, although optically both are pretty close. I bought the Burris binos for my wife, and they compare fairly well with higher cost binos other than the fact that they require more focus adjustment over varying distances. Having to adjust focus more when distances to the objects vary is a disadvantage to some extent but can also be an advantage when looking at objects where you want to blur the focus in front of or behind the object (like looking for animals in forested areas) or where you are looking at mirage waves for doping wind in long range rifle shooting. There are other good optics in the mid-price range too, and all of the high priced binos are good to excellent, as you would expect. Also, we all know that being unwilling to pay much results in not getting much. In the world of optics, $150 isn't much.
Allan