Am I missing anything? I don't need a keyboard/mouse, videocard. A wireless card would be nice but not needed.
Threads like yours pop up twice a week. A list of specs and then the question "Will this run all/most games". I think people are getting tired of answering the same question.
Try reading some of those threads first. They should contain more than enough information to answer your question.
Basically they all say if you have a average current pc with an average current videocard, you should be able to run most games.