Good job setting that up. I claimed an offer for a month of boxing cardio classes at a gym by my house. I got taught the basics of throwing punches and moving, learning to love/hate the jump rope, and get some great workouts in. Normally $50 to $150 a month for regular training from a place like that, I found my deal at $25 for a month. I would recommend searching online for a 1 time monthly deal like that, to get a professional supervised workout plan, then take it home and do it yourself. Since my fiance is also looking to lose weight, we found a deal at a closer boxing/mma gym for $57 combined. we also dont have the room or equipment like you so that works for us. Good luck, I've found that boxing type training to be some of the most "bang for the buck" training you can do.

..not familiar with the weight machine, but I sometimes do a heavy bag wokout. If you search youtube heavy bag workout videos, you will find hundreds of them. The one I use is:

30 secs light tapping punches, jogging in place getting your knees as high as you can (if you look a little silly you are doing it right)
30 seconds rest
30 seconds medium jabs moving around while throwing punches
30 seconds rest
30 second haymaker punches, near max effort
30 seconds rest
Rinse and repeat 5 or 6 times, go lay down.

My kids have some junior boxing gloves, and they alternate in while I am resting.
Some tips:
Use longer rest periods when starting out
Use boxing gloves! And some sort of wrap under the gloves
Have fun!