There are many weapon types in Advent's setting. This is what you can claim your character has without any need for approval.
Almost anything. Keep the kind of setting Advent has in mind and you can barely go wrong.
Once again, keep the setting in mind. The way technology is developed there is some pretty heavy weaponry and firearms available.
Please check with an ST if you're unsure that your particular weapon may be acceptable or not. It never hurt to ask in advance rather than being warned later on.
What you can't have without an approval
Basically anything over the top, completely ludicrous or that clashes with the setting. Advanced technology does exist, but it isn't available to everyone.