How to make a good full body strength training routine?

Are you looking for free weight advice, bodyweight workouts, advice on which machines to use, etc? For a beginner bodyweight workouts are (in my opinion; I am not a fitness expert and can only speak from my own experience) the absolute best. Pushups work the arms, core, back, and to a lesser extent the legs. Planks target the entire core. Burpees are a good exercise for building explosive strength. Pullups are the mother of all arm and back workouts, and also use muscles further down on the torso, and even the legs to a limited extent. There are dozens of other exercises you can do with just your own body weight that build total-body fitness, and the best part is that they don't require anything other than your body, a solid surface to stand on, and maybe a low chair or bench in some cases.

I'm gonna do it 3X a week, regular cardio 3 days, and the 7th day is a rest day.
How do I figure out which exercises, number of sets/reps would work for a beginner? Thank you.

Instead of trying to create your own, maybe look at Starting Strength or Stronglifts 5x5 programs. The New Rules of Lifting for Women is also a good read i've heard

Ditto.

They've already been made for you. Starting Strength is the strength training program. I'm not familiar with Stronglifts 5x5, but I used Madcow's 5x5 (google it and they have have a nice spread sheet that will calculate what your next lifts will be. The only thing about Starting Strength is that the Power Cleans are difficult to master without someone checking your form.