First, good on ya for using your skills to make this for your church! I like the square tube turned 45* idea.
As to which process, either way you're going to want full penetration welds. It may turn out that the place you weld it in drives that decision: outside in the wind? Stick. Back at the shop in ideal conditions? MIG. But now may *not* be the time to experiment with a new process like dual shield: the final exam is not the time to learn the material.
Don't get me wrong, I'm totally with you: learning, experimenting, figuring it out is the fun and compelling part of any project. I get it! But as they say over on WW, the last thing you want to do is injure any nuns/widows/orphans/puppies because the welds on your cross failed.
That said, and with safety and longevity in mind, I don't think you can over-think this. I did some checking, and found that 8" square tube in 3/16 wall is 19.63 pounds per foot. If the vertical is 12 feet and the "arms" are 6 feet, your cross could weigh as much as 350 pounds. Where and how will this be mounted?
The way you design it can affect the overall weight and the amount of stress your welds endure. For instance, you might start with a 12 ft. vertical and weld the "arm" members to each side. Gravity will be pulling on those welds forever and ever amen, and those stresses will increase every time the kids from the youth group climb up on your cross. (Count on that, btw!) On the other hand, you might start with a 8 foot 4 inch vertical, and lay a single 6 foot horizontal member on top of that. That way gravity is pressing the horizontal down onto the upright, and your welds are holding it together rather than keeping it from falling apart. Finish with a 3 foot "INRI" top part of the cross. (And cap the exposed ends to prevent internal rust and bird nesting.)
How's that for preaching to the welders?! Sorry if you knew all that already. Good luck with your project, post up some pics!