If what you mean by "CQC" is what real military forces use to disarm and disable opponents, you can either go with the actual combat training they do (Semper Fu, for the humorists among us, or Krav Maga and its derivatives), or you can go for the style a lot of those are based on, which is Aikido.
Which fighting style is preferable depends a huge amount on a couple of factors. First, what type of combat are you interested in doing (and this is completely personal preference); there are striking styles, grappling styles, and hybrid styles. You also have to pick a range for combat. Aikido is very up-close, so is Sambo and most grappling. For striking, you can pick a range more; Shotokan Karate (what I do) is a mid-range style, with a lot of punches, TKD is a longer-range style. You also need to pick whether you want an offensive style or a defensive style; traditional Aikido is a defensive style primarily, Shotokan is more offensive (once combat can't be avoided). Lastly, there's a choice of how you want to move your body, what makes sense for you in terms of getting power in your motion. Shotokan comes from the hips (a side-to-side motion), TKD comes from the legs (up-and-down momentum), and Aikido comes from leverage.
On the question of weapons; an Aikido Sensei I know described it best (in my opinion): the person who has the fewest rules and limits will be the one to win the fight. All the training in the world doesn't matter if you can't bring yourself to use it, and a lack of training matters less if you're willing to be absolutely ruthless. If one person wants a battle on the field of honor, and the other just wants to walk away, the second will almost always win.