Best thing to do would be go down to any local pro shop, tell them what your situation is, give them your price range, and pick out a bow you feel is right for you along with the help of the employee working at the time..As myronman said,you dont need an expensive bow to kill deer, but some bows are made better than others. Unless you know for sure your going to be serious in archery I would start off with a "lower priced" bow, but if your sure you will be serious about it..hey, why not go with a higher priced better quality bow that you know will last you a long time, if your not sure..and dont want to spend the money I recommend a Dartin,PSE,or Fred Bear....If you feel that you want to spend more, I would go with a Mathews or Hoyt..both top of the line and highly recommended bows..Im not saying you cant be serious and have an in-expensive bow, and to quote myronman again...expensive bows dont kill deer, well placed shots do..
Good luck with your decision..and keep us posted