Newbie looking for workout advice

Hi there!

I've been a lurker for awhile but I'm going to jump on board in 2013 and dedicate myself to getting in shape and eating clean. I'd like to start by losing 20 pounds (my pre-pregnancy weight) and then go from there. I know that diet is the big part and I know what to do there its just a matter of doing it :)

I kickbox at a martial arts center 2 times a week. One of the classes is 90 minutes and the other is just an hour. I can't really justify a gym membership at the moment but the kickboxing club has some free weights and a few cardio machines. They also have a TRX suspension thing that I suppose I could learn how to use.

My question is, how much do I need to supplement my hard core kickboxing classes to lose weight and get fit? Any suggestions would be super helpful.