Not sure if I want to make the super power synergy character. But this is also proof I shouldn't do mages. Well back to the drawling board.
You shouldn't be too hard on yourself. Burnout mages are fun and I enjoy playing them. You do want to make sure you're getting your money's worth out of the lost magic.
Really there's two pieces of ware you should consider and almost certainly use a burnout mage. The first is cyberlimbs, full ones especially. Cyberlimbs do 2 important things. The first is make you tougher. Cyberlimb armor helps a lot when people want to geek the mage. If you can get your average body improved, then you might be able to wear more armor and that's even better. The second is that it's pretty easy to make a guy who's okay at gun with a cyberlimb. That's extremely handy in background count which are extra effective against you since you're a burnout mage. It also fits the whole "I was in a terrible accident/gunfight/bear attack and they had to replace my arm with a metal arm" trope.
After armor and attribute enhancements, you can fill out the rest of the limb with cool stuff like spurs, biomonitors, datajacks, gyromounts, or whatever. Cyberlegs can store more stuff; cyberarms are easier to their attributes for stuff like attacking.
The second is Cerebral Boosters. Burned out mages can just go to the store by buy +3 logic. That's really cool for logic traditions. You may or may not want to start with cerebral boosters due to the restricted gear tax, but they should be part of your ware setup eventually.
After that, you can fill up in ware that's either handy like attention co-processors or nifty like sleep regulators. Now you'll have to decide how much you'll likely to lose. In this character's case, you're cool with losing 2 points of magic. I'll get a full customized cyberarm. How great this arm is will depend on how high your avail cap is. Ideally you'll want the arm to hit that cap and get enhancements after that. I would aim for Body 8 and the highest agility you can get after that. The Body will make you tough and the agility is for stabbing/shooting.
Then you can put in a weapon focus spur. That's not my cup of tea, but it seems like yours. After that, you can add whatever you have left. Be sure to leave room for higher rating enhancements! They're pretty cheap but hard to find. If your group has a face or a decent contact like a fixer, they should be able to find them for you once play begins.
With the cyberarm, you can either start with cerebral boosters 3 (restricted gear) or just save your cash. Either way, I'll leave room for it. Umaro doesn't like mages with cybereyes nor do I. However I will admit for mages there's a case to be made especially if you want robot eyes 'cause they're cool. After that, you fill the rest of your essence with stuff you want/think are cool.
That covers ware. If you want advice on skills/spells/other stuff, tell us what preferences/rules you have and we'll be glad to help.