I'm in the early stages of trying to figure out exactly what it is I am doing and would appreciate any input anybody can provide. My goals are, probably a lot like everybody elses, weight loss and muscle gain. I hear a lot of people talking about core training but have never really been able to figure out exactly what it entails. Can somebody explain this to a total newbie to the exercise world? Also, it's been probably a decade since I've really done any physical type activities, there's not a lot of heavy lifting in the tech world, and I am interested in some goood routines for somebody grossly out of shape and completely lost in a gym. Thanks in advance for the help.

Honestly I started out with walking. It's a good fat burner and if you've been out of it for a while it's a great start. A long walk will kickstart things and prepare you for more activity like jogging and running. Just my opinion...

Best thing for you to do is start Slow and build up. If you go all out and get hurt that will just discourage you. Another very important thing is to make sure you have a good Diet. Exercise and Diet go hand in hand when losing weight. Search around the forums there has been some great posts on diets and exercise plans for all lvls.

What are the best lifting excersises to start with as a beginner and somone not worried about body building so much as solid streangth gain?

Stick to the basic compound movements:
Bench Press - Chest, front delts, triceps, lats
Squats or Leg Press - Legs, overall body
Reverse Grip Pull-Downs - (palms facing you) Back, biceps, abs

That is enough to build strength and muscle all around. Stick to 1 heavy set with enough weight to perform 6 - 8 reps. Really emphasize the negative and perform the rep slowly and deliberately. Rest 4 - 7 days between workouts.

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