So strength and speed without weight. Cool.
Assuming you don’t have weights, look up a guy named Ross Enamait. He’s pretty much America’s leading expert on getting strong using bodyweight exercises (and if you ever run into Matt Furey’s work, RUN!).
By ‘don’t have weights’, I mean your current set of beginners weights don’t count. I mean, they go up to what, 40lbs? If you tack all that onto a single dumbell? If you’re repping it overhead, it’s too light for the work you want to do.
Assuming you can either a) get a membership at a gym (there are all sorts of ways to do this that don’t involve money, if that’s your hang up) or craigslist a barbell and weights, you’re gonna have your work cut out for you.
Athletically, you’ll need to develop a minimum level of maximum strength, a healthy bit of anerobic endurance, and unlimited endurance in your shoulders.
CW says it better here: http://www.T-Nation.com/article/most_recent/7_steps_to_a_balanced_fighter
As far as speed itself is concerned, you’re probably referring to the ability to punch or kick with speed, which is a skill you only really develop with practice in martial arts. Weight training won’t do it. Bag work might, if you can’t train at a dojo or school.
Don’t try to cut fat until after you’ve established strength. Everyone wants to walk around with a six pack all the time. Wait on this one a little bit. If you’ve persevered with your training and eating, it’ll be simple down the road to drop fat.
Simple does not equal easy, though.
As for actual programs, I’d recommend Mark Ripppetoes starting strength.
And on off days, do conditioning work (jump rope as CW recommends, do circuits, drag sled, go to MMA practice). Don’t overdo it, and you should be okay.
As for diet, do the AD as planned (plan your food and make sure you’re getting close to the ratios he gives as you can on both regular days AND carb-up days) and continue to eat at BWx18. This should provide enough calories to allow you to recover. The cleaner your food sources, the more likely you are to drop fat and gain muscle (10 oranges are a better carb-up than 1 cup of ice cream).
This is a lot of words. I hope you got something out of it. If you have more questions, keep posting on the thread or feel free to PM me.
I’ll be interested in hearing about your progress. Good luck.