First off red dot sights and low recoil, quick handling carbines are a great combo. Whether hunting or plinking a quality red dot can really be a fun advantage. Being in the Army, I lots of experience with this type of optic. If you are planning on hunting, the ballistics of .357 mag will limit your range more that a red dot sight will. That's for sure. For hogs, deer, and smaller .357 is fine out to about 100 or 125 yards. Even a 4 MOA dot will be small enough for that. Quality sights are more than just quicker than irons, they are also more precise. This is according to extensive studies by the US Army. The Army has determined that they are AT LEAST as precise as m16a2 iron sights out to 300 meters.
The problem is quality red dots are expensive! I have had many different brands at every price point. Ha Dingus suggests the Millet SP1, 3 MOA model. I can agree that its a fairly good option for your budget. But it is made in China and the glass does have a bit of a blue tint to it, some more than others. But mine has been reliable so far, and it takes regular 1" rings. Battery life will be short with sights in this price range so keep spares. You won't have to re-zero after a battery change with most sights. The Burris Fast Fire II is about $200 plus the mount, and it gets mixed reviews. Also there isn't a mount available for the 1894. Aimpoints are at the top of the game. Most Aimpoints can be left on for well over 5 YEARS with out the battery dieing. I bought an Aimpoint 9000L when they were on sale at Midway for $250! It will be going on my Marlin 94 in .357, on a XS scout rail.