I'm assuming you don't plan on being really hardcore, joining competitions in the future? Here is my two cents:
1- Which muscle groups are different? I ask this because if I work my triceps, I may not have enough energy to work my back. Because I think I read somewhere, it says that triceps and back are the same muscle group. So if I work one out, I'll be left with no energy to work the other one.
Arms, Legs, Back, Chests and Shoulders, these are your basic muscle groups. I usually work out two muscle groups at a time e.g. chest & shoulders. I don't find it necessary to isolate your arms that much as with every exercise, you either directly or indirectly work them out. You should avoid working out your back and shoulders at the same time because they do overlap.
2- Is it better to workout weights first, and then do cardio? A few fitness trainers told me that working weights will break down the fats, and cardio will 'wash away' the fats.
A lot of fitness trainers I know have differing opinions. In the end it's simple, it's all about losing more calories than you put in. I've heard fat people say they need to lose weight before going into weight training. That is BS if you ask me. It's simple: The bigger your muscles, the more calories you burn even at rest. A combination of the two is best.
I do doubt the validity of the point you mentioned simply because I am unable to think of a rational explanation as t why the trainer would say that. I don't do cardio anymore having already lost 12 Kg's from watching what I eat and playing basketball and badminton. When I did however, I used to run for 30 mins before working out.
Just to digress, I've met so many people that tell me they skip meals because they want to lose weight. WRONG! In fact skipping meals can lead to you gaining even more weight! Eat right. I eat 4 - 5 meals a day now and I'm not gaining any weight. You just have to avoid stuff like deep fried food, curry, too much rice, fatty food, etc. The more you workout and the bigger your muscles, the more you end up consuming. It's simple really. Bigger engines drink more petrol and bigger muscles need more fuel.
I've read to many articles and opinions and have realised that everyone will have their own suggestions. They are all probably right as well because if you do workout, you will grow, simple. The only difference may be in the time it takes. Also you will meet extreme gym goers that will recommend all sorts of exercises that will work out small little muscles that unless you are really serious, you don't need to.
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