well, they're going to be expensive, I'll tell you that right away. Just going off the book, your weapons are practically more expensive than the mech itself. The good news is that you don't need to do as much damage as you want to do, at least not at first. There will be enemies later on that require that much firepower, but starting off, you don't really need to be able to blow up a moon. That said, I would suggest adding some restrictions, or perhaps adding qualities to your weapons when you and your mech level up.
Swords of Dark Flame: that would be 21 MCP. fairly cheap.
Wrist Mounted cannons: 4d8 (a bit excessive for a starter mech by the way) makes them 36 points, without traits and restrictions. with traits and restrictions, it is 7 * 36 = 252. if you dropped it to 4d4's the cost would be 140. you could also lower the cost if you added some restrictions to it. each quality multiplies the cost starting at 1.5 -> 2 -> 3 -> 4. restrictions reduce it the same way. The unlimited shots quality counts as four qualities, so if you got rid of that, you'd be at 98 MCP. by the way, I counted the two barrels per wrist as one quality.
Ah, the emp burst cannon. damage alone brings it up to 63*2= 126. after restrictions and qualities, you actually halve that. So the emp burst cannon stands at 63 MCP. I'd be okay with a one shot cannon like this. If you were to take slowfiring, you'd drop the cost down to 32. for a weapon like this, I can see such a restriction being feasible.
The mines cost 72. While I can see concealed being a good trait for mines, it's not entirely necessary. You can get rid of that quality and still have difficult to see mines. Also I would suggest holding off on the mines for now. There are places where a creative use of a mine would be handy, but you probably won't have an opportunity to use them until level 2 at least. Then again, since you guys have significant influence on the story, you very well may end up with a chance to use them early on. Either way, your weapon totals, as they stand at the moment, are at 408.
also, please change my name <innocent(?) grin>