Here are a few factoids
Your 3003 aluminum has manganese as it's principal alloying element, as far as weldability goes there are two most favored choices for filler based on the following:
4043 is the choice for maximum strength and crack resistance
1100 is the choice for best color match after anodizing and superior ductility.
6061 (most sheet is T6) is alloyed with silicon and magnesium. Here you have 3 favored filler choices (if your not tied into manufacturers specifications.)
5356 provides maximum strength and ductility
5654 has the best color match after anodizing (I've never used this)
4043 offers the best crack resistence
Now as far as GMAW goes. If you have a push pull gun than your filler choice can be totally performance based. However, if your trying to push your wire through a short gun with a regular feeder, 5356 filler is more ridged than 4043 or 1100. Many welders have experienced great improvement in bead quality and profile just by making the switch.
As stated correctly above, welding itself should not make your 6061 brittle, but contamination, or hydrogen entrapment can, but this is true for most aluminum alloys
Both 3003 and 6061 are formable, just make sure your bend radii aren't too small.
Here is some good forming and general data