I have a set of used 16x58 big eyes that I keep in the truck and use on scouting trips. They are incredible, but I would never ever ever carry them hunting. When hunting I use excellent 8x32 Leica's I bought refurbed well within your budget, don't feel like I'm giving up anything substantial to bigger glass, and love the size and weight. I can tell you this--with any binoc, you see a lot more at distance if it's dead steady. You can use your bow or a stick as a monopod, glass off your knees, or even carry a very light, small tripod with a binoc adaptor. I wouldn't bother with a tripod unless I was doing a LOT of glassing, but it does make a perceptible difference, and the tripod helps you grid out your glassing. If nothing else, I try to rest the binocs against a tree if available and I'm doing more than a quick glance.
Spotters are really for the sheep and goat crowd who need to be very careful in their estimation of horns. Or for the truck.
The good news is that there are a LOT of excellent binocs within your budget--many of them well within. You might check a birder's website called betterviewdesired.com for its dated but excellent reviews. You can also go to the hunting optics forum on 24hourcampfire to read volumes on this subject, some of it from experts.
Western glassing is a real skill. After a pretty moderate level of quality--say in that $250-500 range from one of the better manufacturers--or even below, now that I think about it--the skill is more important than small increments in optical quality. For me, what you're paying for in that middle range and above is near-absolute reliability and ruggedness--which is worth a lot when you're back in the mountains! For a grand, you will get kickbutt reliability and optics that will startle you every time you look through them.
One other piece of advice--save a bit for a low profile chest pack that will keep the dust and rain off them but keep them handy. I probably pull out my binocs 50-75 times a day...