Sheridan's comment is spot on. In your price range, I too would suggest a pump action. This will give you a good value, simple, rugged shot gun that is suitable for hunting about any game that we have here in the US. Once you practice a good bit with a pump, you can make very quick, accurate follow up shots. I ahve used a pump since around 1975. A pump action is my personal preference.

Most will come with 3 screw in choke tubes .... Improved, Modified and Full. Improved is great for wing shooting smaller birds such as dove and quail. Full is great for longer range such as turkey or pass shooting water fowl, or knocking squirrels out of the top of a tall pine. Modified is sort of a "tweener". As mentioned, you can buy a "turkey" choke too. This will add $50-$100 or so to your expense. A turkey choke is more or less an extra full and many are ported to somewhat reduce the recoil of heavy loads typical of a "turkey" shell. As for game like deer, there are "shotshells" loaded with a slug that are designed to fly pretty well out of a smooth bore. These allow a hunter to be effective to about 100 yards.

Shot size is a part of selecting what is optimum for the game you are hunting. The larger the "number", the smaller tha shot. A simplistic statement ... smaller the game, the smaller the shot. Lead shot for example ... doves and quail - 7 1/2 or 8 .... rabbits and squirrels - 7 1/2 or 6 .... bigger birds such as ducks, geese and turkey - 4 or 5 or 6's .... deer and feral hogs - slugs or 0 to 000 buck shot. Where lead shot is prohibited, care needs to be taken to understand what uyou should use. Consulting the information on the shot shell box will help you decide. And stamped on the choke tubes will be information letting you know what the limitations are associated with taht particular choke for use with a non-lead shot might be in effect.

I know this is getting long .... but .... be sure once you have your shot gun to go out and pattern it. Different manufacturer's shells, diffeernt shot sizes, etc. will usually pattern a bit different from one another. You can find a lot of good information about how to pattern and what to look for. Essentially, you are looking for a nice, evenly distributed circular pattern. And you want that pattern to be more or less centered at the spot where you aimed.

One more comment. Don't overlook buying a used shot gun. Very often one in great shape can be found priced well below a new one.

Hope you find a good deal on a shot gun and good luck hunting.