I hate to say this, but you are better off doing whole body training rather than focus on a few muscle groups. The reason I say this is because if you train/build muscle in one muscle group you run the risk of being weak in another and may end up having problems in the long run.
But if you seriously only want to target those 2 areas, I would say push ups (incline if you cannot do regular), bicep curls, triceps dips, triceps kickbacks, dumbbell chest presses, dumbbell upright row and presses for the arms and for the belly - core exercises i.e. dead bug, planks, bird dog, etc., russian twists, crunches (I don't do sit up because they bother my lower back).
If you don't want to invest in dumbbells then think about getting resistance bands - cheaper and easier to store.