If you're not the " best welder" then you should leave it to somebody that is. Welding the tubes requires a process, and somebody who knows what's gonna happen when they put that much heat to the axle tubes is a must.
An 8.8 that has lived a hard life will have tweaked tubes. Some are so freakin bad you can stand over the rear end and see how far forward, or twisted, or forward and twisted each tube has pulled at the brake end. ( usually a rear that had slicks on it)
Welding the tubes, welds dissimilar metals together ( usually never works) but in the case of a ford rearend, somehow seems to work beautifully. The welder you use has to be capable of welding 1/4" stuff, and typically would mean that it's not gonna be a 110v piece. Once the welding process starts, you cannot stop.....The weld bead has to be continuous all the way around, or you'll be able to literally watch the tube move one way or the other as heat from the weld will pull on it.
Unless you plan to drag race the car regularly with sticky tires I'd probably pass on that though..the same for the brace that you've pictured.
On the other hand,....if you do intend to drag race it weekly, than do both....welding the tubes will not stop them from bending,..the brace will. That brace is intended to do both w/o welding the tubes, but if using it, I'd weld the brace on, and forget welding the center to the axles.