Mike,
Welcome to the board! Youll find all kinds of useful info from the members on this site, and you dont have to worry about askign beginners questions, we have all levels of competitors on this site. First ill try to briefly describe some of the terms you listed above, and hopefully it wil help you get a better idea of what all of that means.
Balance training, is basically any number of specific exercises that will help to strengthen your legs and ankles, and help you to keep your balance centered in your boxing stance. My trainer likes to use a tire, which you lay flat on the ground, and stand on the sidewall and work your way around the tire.
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Im not entirely sure what you would mean by skill training, other than slipping and ducking, and possibly blocking and parrying punches.
Most of a boxers regular workout is centered around conditioning, and muscle memory. In my gym, we work a bag for 5 3minute rounds, taking one minute inbetween for rest. Here is the usual workout I do, with variances here and there:
Start with 20 minutes jumprope
4 rounds on the speedbag
5 rounds heavybag
3 rounds uppercut bag
2 rounds double-end bag
4 rounds on the cycle
finish workout with calastenics (pushups/situps/jumping jacks/etc)
As for the strength training and core training, they are pretty much one and the same. Core exercises include squats, deadlifts, and bench press among others.
Plyometric training is more for explosiveness and speed. It helps to develop the fast twitch muscle fibers. There are many different exercises you can do with a medicine ball, or light weights to help achieve this. Plyometric training is more low weight, with a concentration an quick, explosive movements in the workout.
Shadow boxing is basically a visualization of you boxing an opponent. You practice your footwork, and stance while throwing punches at an imaginary opponent. It helps you to develop muscle memory, and keep yourself disciplined in the way you stand, throw your punches, and defend yourself.
I HIGHLY recommend the title boxing DVD series. Its very informative and easy to understand, and apply to your workouts.
Once again, welcome to the boards and keep the questions coming. There are alot of guys on here with great tips for you.