If you don't have any friends/relatives who can show you some things, you might want to consider a small personal training package. Personal trainers are expensive though so if you have to go with that option my suggestion would be to buy the smallest training package possible and ask them to put together a basic weekly upper body routine for you. Learn the form and technique of those exercises they show you, run through the routine with them for a few sessions, then dump the expense of the training sessions. Once you're comfortable and confident in the exercises they show you, there's no need to pay them to stand and watch you do what you know how to do. From there, get to know people in the gym, observe different things that different guys do, pick up some tips and tweak your routine along the way.
I could give you a laundry list of exercises, but you'd be much better served having someone show you how to do them. Proper form is critical, both in achieving results and preventing injury. Your shoulders are particularly vulnerable to injury during various shoulder and chest exercises. If any exercise gives you uncomfortable pain, particularly shoulder pain, stop doing it. There are all sorts of different exercises you can do to target a specific muscle so avoid the exercises that cause pain.
As for the fat burning - including the stomach fat - my best suggestion is to do various HIIT cardio immediately after your weight resistance workouts. Sprints work very well. Bikes aren't bad either. Just make sure to stretch thoroughly before and after. Throwing in some HIIT sessions after the weights will spike your metabolism for the rest of the day. This means that after your workout when 7pm hits and you find the couch to watch the Reds, you're still burning significant calories and fat.
Diet is paramount too so if you want some diet tips just let me know.