TellMeMoar saidI dont know about bowflex. Machines have their place but I prefer to use free weights.
gaining = caloric surplus
losing = caloric deficit
If you are in caloric deficit you wont be able to gain and lose at the same time. If you are a total noob to training or have resumed training after a long haitus then yes but it is only for a short time at the beginning.
Anyway, since you are trying to lose fat and retain muscle as far as possible, train heavy.
So by train heavy up the weight and the amount of sets and reps? Great.
I want to gain muscle in my arms and chest but that might mean having to eat more and I don't want to risk gaining more fat.
As a newbie you will probably lose weight and gain muscle at the same time for a fair while. But I think you should definitely focus on cutting first. Which, as TMM said, involves a daily caloric deficit. Count your calories, which I've noted before.
Belly fat, for many folks, is the last fat to disappear. So be patient.
Personally, I suggest that you also cut way back on the carbs. First of all, stuff like pasta skyrockets your blood sugar and keeps you wanting to eat more. Second, it's really calorically dense, which you'll find out if you start tracking. I don't "believe" in Paleo, per se - I think there are many "Paleo" guys who have terrible diets, who view it as excuse to eat way too much of the wrong thing. But I do think that some carb restriction is probably a good idea.
When you train heavy, that usually means heavier weights, but lower rep ranges. You can't do both, something has to give.