Gears and a camshaft with a good tune. Buy from a highly reputable company like texas speed or comp cams. The 2008-2012 5.3s had a lot of variables, things like variable valve timing, and displacement on demand, these can be tricky to navigate when it comes to power adders. But the big companies have already worked out all the bugs and can be as reliable as stock, assuming you don't abuse it too much. The 5.3 you have can easily be taken up to 400hp using a cam and appropriate tune. In fact, it can be done with factory gm parts if you do a little research. But again, depending on the specific options you have, sometimes its just easier to go aftermarket. Texas speed has a couple really good cams/tune kits. You mail them your ecm while you do the cam swap, a couple days later it comes back in the mail, you plug it in and go try to enjoy the power without breaking anything, good luck whipping the smile off your face!
As for the tranny, add a big cooler. The gears will help a bit. But eventually, trannys die. Heat is always enemy #1. But new ones can be had that can handle 5-600hp all day.
as for what gears, i agree with 2 buck. Get some 4.10s.
all of this will be cheaper, and more reliable than a blower. Dont get me wrong, blowers of any kind are awesome fun. But pricey and risky. Just depends on your goals.